The Bird and the Bees of combat training is basic personal infantry and squad level fighting infantry skills and tactics. The Elephants and Giraffes adept training and qualifications expand on and build on being proficient in the basics. If you are not proficient with the Birds and the Bees you do not progress to training in the higher skilled tasks and qualifications.
What exactly are you asking? Weaponry is generally specific to weapons and combat training generally involves tactic, technique, and procedure (TPP). The basics of combat training is such things as land navigation, shooting proficiency, combat patrolling. The adept skills and qualifications might include such things as tracking skills, SERE Skills, military mountaineering skills, arctic warfare skills, urban warfare skills.
The play on words is being used because within the Air Force the combat career field demarcation is classification of Battlefield Airmen and within this classification there is some distinct employment concepts demarcation of supporting the Army and being a war fighting asset or capability provided to and employed by a combatant commander for the accomplishing of achieving a specific on the ground battlefield participating in a tactical combat mission role.
Back in the day we got to shoot (our mouths off) using a KWM2-A, or a TSC-15, or etc,etc. Shooting the "big boy toys" simply wasn't our job. We had to qualify with the M-1 carbine & the M-14. Now I suppose it would be the M-16 & M-4. I would imagine that very few will go beyond that with weapons training.
The idea behind most combat training for these AFSCs is to keep us from becoming a liability instead of an asset (while we are doing OUR job), so hopefully you will learn enough to keep from getting someone killed.
At a minimum a TACP must be proficient with his M-4 and M-9 and have familiarization with various crew-served weapons. Proficiency on these is highly encouraged. How proficient you become is up to your supervisors and the level of training at your unit, specialty courses you may attend, and ultimately yourself.