my favourite thing about tries is that they sit between lists of strings (cf extension/intension; tries are possibly exponentially better!) and finite automata

my favourite thing about tries is that they sit between lists of strings (cf extension/intension; tries are possibly exponentially better!) and finite automata (which can be useful if one wishes to share tails, and become necessary if one wishes to encode infinite sets in finite space) (can one hit all of these CS concepts by examining only two data structures? or is this path via tries didactically minimal?)