help with sequence prefixes

Suppose sigma and tau are arbitrary sequences over some set A.

Is it true that sigma is a subset of tau if and only if sigma is a prefix of tau?

I want to show a counter example sigma is a prefix of tau but not a subset, but I don't understand how that is possible? If something is a prefix than its exists in the other, so it has to be a subset.

I could show something is a subset but not a prefix, but I don't know how to show an example of a subset with sequences. I can show it for sets.