Or, for that matter, are there any significant occurrences of two cultures having developed the same concept independently?

For example, I learned recently that Italian and Sanskrit share a similar word for snake: serpe and sarpa, respectively. From this, I could conclude that there must exist some greater language connecting them (which, if I understand everything correctly, is the Indo-European family of languages). However, in the absence of other historical context that may link the two cultures together, it can also be concluded that this is a simple coincidence, rooted in the fact that snakes hiss and it would make sense for words that describe them to make use of the "s" sound.

Is there any reason to suspect this might be the case? Have two cultures developed something completely independently of each other, or is it always the case that cultures with some significant commonality must share an ancestor? Is it possible to distinguish between these two cases in the absence of further context? If not, and maybe this is too vague a question, but is there a well-established or widely-accepted notion of "enough" context to link the two together (outside of hard evidence)?