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 $\Sigma$.
Sequences' elements are indexed with natural numbers N.

Tuples' elements are indexed with positive integers N*.

Sequence is use to define relations in general
(i.e. where the cardinality of arbitrary sets is not clearly identified).

Tuple is use to define finitary relations in particular
(i.e. where the cardinality of finite sets can be directly identified).

"While the cardinality of a finite set is just the number of its elements, extending the notion to infinite sets usually starts with defining the notion of comparison of arbitrary (in particular infinite) sets." From Wikipedia, the free encyclopedia.