I'm learning about radix trees (aka compressed tries) and Patricia tries, but am finding conflicting information on whether or not these two are actually the same. A radix tree can be obtained from a normal (uncompressed) trie by merging each node that is the only child with its parent. Apparently, the same holds for a Patricia trie. But in what ways are the two structures different?

For example, [NIST][1] lists the two as the same:

> **Patricia tree**
> 
> *(data structure)*
> 
> Definition: A compact representation of a trie in which any node that
> is an only child is merged with its parent.
> 
> Also known as radix tree.

Many sources on the web claim the same. However, apparently Patricia tries are a special case of a radix tree. [Wikipedia][2] entry says:

> PATRICIA tries are radix tries 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.

but I don't really understand this. Is the difference only in the way comparisons are made when doing a lookup? How can each node be a "two-way branch" - shouldn't there still be at most `ALPHABET_SIZE` possible branches for a given node?

Can someone clarify this? For practical purposes, are radix tries typically implemented as Patricia tries (and hence often considered the same), or can no such generalizations be made?


  [1]: https://xlinux.nist.gov/dads/HTML/patriciatree.html
  [2]: https://en.wikipedia.org/wiki/Radix_tree#History