I know that they both refer to noodles, but would they be different kinds of noodles? For instance, one might be long and thin, while the other might be flat and wide?
In Spain, at least in my region, Andalucía, it's quite different.
"Tallarines" is a type of pasta long and flat, but we referred that only in the asiatic case. In other cases, we used the italian word "tagliatelle".
For "Fideos" we understand the kind of pasta you use in a soup. Usually they are tiny and short:
For the long and thing kind we use "Espaguetis".
The answer to your question will depend on the region you want to go.