I understand that they are implemented differently, but what is the difference in terms of functionality?
The Google CardDAV API lets you access the Google contacts API using CardDAV protocol.
vCard Extensions to WebDAV (CardDAV) is an address book client/server protocol designed to allow users to access and share contact data on a server.
The Google contacts API is itself a Google Data API protocol.
GData (Google Data Protocol) provides a simple protocol for reading and writing data on the Internet, designed by Google. GData combines common XML-based syndication formats (Atom and RSS) with a feed-publishing system based on the Atom Publishing Protocol, plus some extensions for handling queries. It relies on XML or JSON as a data format.
What is a protocol:
protocol In information technology, a protocol is the special set of rules that end points in a telecommunication connection use when they communicate. Protocols specify interactions between the communicating entities.
What is the difference between Google's Contacts API and CardDav API?
The difference is the protocol used to access the data.