Hi Elizabeth
Well, this is difficult to explain but I will try.
"Tal vez" and "quizas" have similar means but in my personal opinion there are a little differences between them, let me explain:
1 Quizas sounds more likely than tal vez ( when you are planing a event, but quizas is more informal)
Examples
* Talvez hagamos un reunion con mis amigos ( 50 % de probabilidad)
* Quizas hagamos un junte con mis amigos ( 60 o 70 % de probabilidad)
Obvious depend on how you say it
2 tal vez sounds better or more friendly in some cases.
Examples
* Tal vez pueda ayudarte ( 50 % de probabilidad)
* Tal vez pueda hacer algo por ti
* Quizas pueda ayudarte ( sound like you don't want to do it)
* Quizas pueda hacer algo por ti