Question about the difference between radix trees and patricia trees
Quoting Wikipedia:


  PATRICIA trees are radix trees with radix equals 2, which means that each bit of the key is compared individually and each node is a two-way (i.e., left versus right) branch.


According to Wikipedia, Patricia is just a "brand name" coined by Donald R. Morrison, standing for Practical Algorithm To Retrieve Information Coded In Alphanumeric.

Patricia trees thus accept their input in the form of binary strings. If the input is a word, then it is first encoded in binary.

As for the smile/smiled/smiles example, it is explained in the linked post – each of these words is encoded as a binary string, and this is what the Patricia tree sees. It is completely unaware of the semantic interpretation of the bitstring as an alphanumeric word.