What's the difference between tuples and sequences? Both are ordered collections that can have repeated elements. Is there a difference? Are there other terms that are used for similar concepts, and how are these terms different?

A sequence requires each element to be of the same type.
A tuple can have elements with different types.
You can compare it with arrays and structs in C (respectively).
For example, let's consider the DFA $(Q,F,s,\delta,\Sigma)$ quintuple. It's a tuple with the full set of states $Q$; a set of final states $F$; a starting state $s$; the state transition function $\delta$ and the alphabet $\Sigma$.
