I heard all those names. In IOS (upper case’i’) the v4 s/w forwarding plane talked about tries. The v6 code was sprinkled with radix. Variable tree stride for different address mapping characteristics was my favourite. I was, and still am, lucky enough to work with the guy who wrote much of that code.

The usual terminology is,

* trie is the basic data structure, in which each node is a vector as wide as the alphabet, and the depth is equal to the length of the keys

* a radix tree is an optimized trie, with path compression and node compression

* a patricia tree is a binary radix tree