What type of connection is this to my spigot?
That looks to me like a factory-crimped assembly, all part of the frost-free spigot. It's designed to optionally allow a sweat (solder) joint, as you have with the street ell, or a threaded connection. 

I'd de-solder the ell and start fresh from the length of pipe in the foreground. You could also clean up and reuse the elbow if your new spigot happens to have the exact same length and configuration.