In a lot of languages that have a character for zero, it basically looks the same even though all the other digits look different.
So what you're referring to is basically a circle. That is the sort of standard character. A number of removed comments have pointed out that it's far from universal, and indeed your examples aren't quite on point, but the general trend stands.
First, to clear up some of the criticisms of the premise.
My own academic background is in Sino-Tibetan, Arabic and a splash of Tai, so I'll stick to those, but I'm also going to rudely tag /u/gingerkid1234 so that he can come talk about numerals in Hebrew and Yiddish.
Yes, in Chinese we have 零 ling and yes that can be zero, but we also write it as 〇 and 0, so even in Chinese it's fair to ask why it is what it is. And anyway 零 doesn't originally mean zero, but rather a non-zero less-than-one value. Another way of writing zero was 空 kong, "empty". There are also what are effectively military numerals (think NATO alphabet for numbers) for which 0 is 洞 dong, which means "hole" or "cave", hence its use here. Again though we'll skip that and stick with 〇 for now.
Arabic isn't a circle for 0. The number is written ٠, a kind of dot. The thing that looks like 0 and confuses undergrad learners is ٥ which is the numeral for 5 (also written ۵ in Eastern Arabic numerals)
Thai is ๐, and while you didn't bring it up, Burmese is ၀ (which will look like one of three things depending on what font you have for Burmese, if any: A circle, a circle with a dot in it, two C's face to face, all in order to distinguish it from ဝ, which is like W)^1
In addition to these single glyphs, we can also write out the words (except in Chinese). So in Thai it's ศูนย์ /sun/ coming from Sanskrit शून्य śūnya. In Arabic it's صفر ṣifr, from which we also get the English word "cypher". The word in Sanskrit has a synonym, सिफ़र sifar, which should look familiar because it's the same word as in Arabic. In Burmese it would be သုည /θòʊɴɲa̰/, which is also the same word.
Chinese 零 is cooler because I'm biased as hell. The top half is 雨 which is a picture of a cloud with rain drops and seen in other cloud-related words like 雲 (cloud) 雷 (thunder) and 電 (lightning and by extension, electricity). The bottom component is 令 and is just there to tell you how it's pronounced (ling). It originally meant a drizzle of rain. As in, it's not straight up raining, but there's a bit of something going on. It was used, numerically, to indicate a skipped significant digit.
So maybe you're asking why I'm spending so much time on etymology. There's a good reason for that. Basically: Zero hasn't been invented too many times. Like written language itself, the concept gets borrowed and adapted and the most typical way that happens is that people straight up take the word as it exists in their neighbours language and, after a little bit of work on the pronunciation, use it as their own. There are exceptions, like in Chinese, where 空 kong meaning 'empty' gets used because it's just a description, and 零 ling meaning leftover rain bits gets used and eventually becomes the go-to word for the concept, but neither of these are conceptually identical to the concept of "zero"; both are borrowed and in some contexts retain their other meanings. In this sense they fail the test of "basicness" that we (linguists) apply to other concepts in a language. These exceptions aside, and actually once we look at the more usual way of writing 零 (i.e. a round thing), what we see for zero is a lot simpler:
The concept, and with is the way it's written down, is similar cross-linguistically because people borrow useful things and zero is useful. (tl;dr here for the lazy)
Numerals in general get borrowed a lot, and even in languages like Burmese and Thai and Hindi and Arabic and Chinese where we have our own numerals that work just fine, we often end up borrowing what is a more universal standard, i.e. 123456790. There are obvious marked examples, such as when King Rama IX passed away recently, the 9 that is his number of Rama-sequence was written in Thai as ๙ rather than as "9". It worked as a sort of a brand, and for the one year of mourning, it was everywhere in Thailand to commemorate his life. Likewise, the use of the Roman numerals in his name just now would be a marked use of an otherwise uncommon numbering system. This is a cross linguistic phenomenon, and we have it in English as well with our frequent appeal to Roman numerals.
I wrote on Arabic numerals last month including some information on the process of borrowing into Latin (and thus English), and the same are used in South Asia, which in turn has some influence on SE Asia. Of course there are other numeral systems such as the so-called Suzhou (or Hangzhou) numerals and the Brahmic numerals which are not derived from a common ancestor with the numerals we use most often today. Still, for the most part, borrowed. In Europe, you can mostly blame Fibonacci.
To summarise somewhat, in Southeast Asia, you can basically say that numerals came from Sanskrit/Pali which used something like either ० or ٠, reflecting emptiness or acting as a placeholder. Likewise in systems like Chinese where this was not an early borrowing, either other placeholders were used, or a gap was left in notation. Europe got their numbers from the Middle East. Arabic already had ٥ in use (coming from ه in one theory) and so used ٠ as the neutral placeholder. Brahmic numerals had no 0 and we see ٠-like notation used in old inscriptions. In cases like Chinese, 〇 is a borrowing. It is not the only character that has been proposed over time to be written 〇; Wu Zetian 武則天 proposed it to replace 星 "star".^2 But as zero it's a clear borrowing. With the domainence of the Western Christian calendar and western colonialism & trade, the numbers used by Western historical powers (1234...) spread throughout the world, and with some exceptions (e.g. you can go a week in parts of SE Asia and never encounter them), they are for better or for worse now the standard.
even though all the other digits look different
This is actually not really the case if you look at the letters a little bit more historically. A lot of the numerals that are used in various different writing systems still have common origins for the numerals. However, as all writing systems become heavily stylised over time, this too causes the numeral forms to change. As a sort of example, Burmese and Thai and Hindi^3 have writing systems which look very different today, but which have common ancestry. Thus Burmese က and Hindi क are derived from a common parent. Likewise Burmese ဉ and Hindi ञ are of common parentage, but Burmese has become much more circular and lacks the top line found in written Hindi but not in related scripts like Gujarati, for which it's ઞ. You can see the similarities here. This is true for most South and Southeast Asian writing systems which are all derived from a much older script. It's for this reason that ယ in Burmese, យ in Khmer, ய in Tamil and ය in Sinhala are all similarly-shaped and represent the same sound.
The numerals and letters look different, but follow similar constraints, and the differences are largely stylistic, hence why Russian has many letters directly borrowed from Greek^4 despite them today looking quite different.
Writing really hasn't been independently invented all that many times in Human history.
tl;dr (recap)
Because of borrowings, sometimes willing and sometimes through colonial imposition. Often the latter.
See also:
There's a book from ages ago, about twenty years back now, called The Nothing That Is. I read it when it first came out so can't really give a point by point critique, but as a pop history I recall it being pretty alright, and would recommend it if you felt like reading a whole book on the subject of zero but one that didn't require a degree in paleography or philology.
Tangents: (footnotes)
A lot of scripts actually used letters to write their numbers. Arabic did this. Hebrew did this and probably still does for liturgical stuff. A lot of scripts also have numbers that look a lot like letters. There's a reason that on old computers 0 sometimes had a dot in it or a line through it or some other feature that made it distinct from O. In Burmese, this is also the case, but there's not a clear standard. The W letter ဝ is almost identical to zero ၀, and on old Burmese typewriters, it was completely identical. Modern font makers have made an effort to make it distinct, and so in the font that Reddit is using for this text box, it's got a dot in it. Another common approach is a broken circle. Regardless, in regular prose, especially in a script like Burmese where spaces are a little less regulated than in English or German, it could be ambiguous what was meant. Easy shortcut for typewriter manufacturers back in the day, but not something that we need to continue with modern computers. Now if only everyone could just agree to use Unicode...
She made a bunch of characters and they're all great but they didn't last. There's a whole wikipedia article on it if you're a Chinese learner and bored. We need to bring back 圀 for 國.
Hindi is the language, Devanāgarī is the script. Devanāgarī is also widely used for Sanskrit. When I say Hindi here I mean Devanāgarī but not everyone knows what that is, so for ease of reading I'm saying Hindi. Don't @ me.
This is a major oversimplification. There were a lot more intermediate steps, and I'm no Slavicist to I'll leave that to people like user rusoved, or your Google-fu. Suffice to say there is a line of descendency there, and for the sake of our purposes here we can say directly borrowed.