Incident Command System
Because of rather spectacular screw-ups where multiple departments were operating mutual aid at big fires and did the wrong things because their codes didn't match the "home" department's codes, the NFPA established the ICS. It came out of the military, went to the fire service, then back to the military, then (when FEMA got ahold of it) was mandated as a national standard.
Because of that, you should not ever hear a fire dept. use any codes at all. One of the very first recommendations was to say everything in plain English to avoid misunderstandings.
You'll still hear some "old-timers" or vol. depts. that use a few, and some departments have some "code words" for things they don't want over the air. And of course they still use abbreviations for some things (MVA, etc.)
I've been listening to TFD for 9 years now and never heard a 10-code.
BTW, PD and EMS are supposed to use ICS as well - but they pretty much ignore FEMA.
If you're interested, FEMA has free online courses (basically just a downloadable book) on ICS. ICS is what you're hearing with all the "1st unit on scene - investigating - passing command" and "Engine xx 2nd on - establishing 31st Street command", etc. It's all explained in the ICS courses. Very straight forward and clear, and it makes sure everyone always knows who's in charge and who's responsible for what.