Oof. This is a big question. I'm not even sure how historical the answer is actually. The shortest answer is we don't know. Just a general we don't know to both questions. The long answer is as follows.

Ok. To start with... what's a word? This may seem easy if you are a literate user of an alphabet, most modern alphabets, like the Latin one I'm using now, make spaces between "words". So in written language, we can just define a word like that, something separated by spaces.

It takes only a few seconds to find some holes in this definition. Just using examples from English, what about compound words? Is videogame one word? Or is it two, video game? And how many words in video-game? What about contractions? Is I'm one word? Or is it two? And if you're illiterate or use another writing system that doesn't have spaces, do you just not have words?

Ok. So our first definition pretty much only works in the context of writing. What about one built on oral speech? These spaces often correlate with pauses, so a word is a unit of speech that is broken off by pauses. Here we run into problems once more, in that we often don't pause between words. Think about a phrase like I got it. Do you really pause between got and it? In normal speech, probably not. In fact, if you're like me, you not only don't pause but the /t/ at the end of got behaves more like the /t/ in the middle of water than a boundary.

And in English, you might be able to put those pauses there, but you could also put a pause after un in unusable. Is unusable two words? And in other languages, such pauses are not really permitted, in French, j'arrive (roughly I'm on my way) cannot be separated into * je arrive in the same way I'm can become I am. And it's not really useful to have a definition of word that only works for one language.

There have been many more attempted definitions, including ones based on whether you can place other elements in between two things, than that's a word. So in French, you could say J'y arrive (I'm on my way there) so j(e) is a word, because you can add this y between it and arrive. But this has its own problems, can you think of a word to place between going and to in I'm going to see him later?

So because no one can settle on a satisfactory definition, linguists have, to some extent, done away with the word word, at least in terms of a clearly defined technical term. It's still used informally to refer to a unit of language that is used on its own and has a distinct meaning, but that varies a bit by language and context and whether it's referring to spoken or written language, ex. in writing, going to might be treated as two words, but in speech, pronounced /gənə/ (gonna), it might be treated as one.

However, if we're talking about meaning, linguists use the term morpheme. Morphemes are the smallest units of language that contain meaning. So videogame, video game, and video-game all have two morphemes video + game, as does I'm. You can take these morphemes and put them in other places and they have meaning. We also distinguish between bound and free morphemes, free morphemes can stand on their own, so video and game can be placed elsewhere on their own and have meaning. Usually combining free morphemes is referred to as compounding and their products are compound words.

However, bound morphemes are units that cannot stand alone. So, in writer, we have two morphemes, write + er. er would be a bound morpheme, it cannot stand alone, it needs to be attached to something else. Bound morphemes are used in two main ways, to derive and to inflect. Derivation is a process by which we create new meaning, writer has a different meaning from write.

But often, bound morphemes can be used to inflect as well. Inflection is when we change a word "grammatically", this change does not change the meaning of the word, so, for example, the bound morpheme s as in writers. Or the other bound morpheme s as in writes. Now, that line between changing the meaning is fuzzy, but generally, when we use bound morphemes to derive, we consider the two words different lexemes.

A lexeme is an abstract concept of meaning, this might also be considered a word. So for example, write and writer are different lexemes, they have different meanings. While, write and writes are not different lexemes. Lexemes usually have a specific form called the lemma that is used to encompass all the different varieties of the lexeme, it's also called the dictionary or citation form because it's the form used in a dictionary. So, for example, write is the lemma for writes, writing, wrote, written.

What's interesting is that when I explained the word morpheme, for example, I didn't have to explain what morphemes meant. I used it just after and you understood that the s meant I was generalizing about the concept morpheme. I also used it after two morphemes, no confusion. You can roughly define inflected forms as those forms which are obvious to a user of the language.

However, derived forms might be more opaque, so when I say morphology, you might understand that it's made up of the morphemes morph + ology, especially if you know that eme is a common morpheme (hence lexeme and also phoneme), but you might not know exactly what it is. I probably have to tell you that morphology studies the way morphemes interact in a given language.

Adding a morpheme, called affixation, isn't the only way of inflecting, by the way, there are other ways, for example, vowel change, known as ablaut, like the inflection that produces wrote from write.

So, when we're talking about a word as conveying meaning, we usually mean a lexeme. An abstract concept that we then modify through inflection and other grammatical processes. The lemma form of the lexeme is what you see when you open a dictionary.