WTF that's all about dept:
With tricep extensions, bottom position, the muscle is being stretch beyond normal function. Lot of applied direct pressure , in this regard. With benches/dips, or any other kind of presses, the triceps are not being stretch (usually) to the full extreme. Also, with any pressing, other major muscle groups (pecs, delts, etc) are taking a lot of direct pressure/workload off the triceps themselves. This allows these exercises to balance the function as a unit, as all muscled do. Dips and Close Grip Benches are excellent compound movement that can target the triceps strongly.
A burning feeling , around the elbow, may suggest the start of the point of undo stress with the muscle, tendon or ligament. Which may/may not include elbow joint problems (at times, the angle/position of the elbows can be corrected, than direct stress is lessened). .
As trainee's advance in age, these sort of problems seem to compound themselves slowly. May have been doing forms of tricep extensions for years, no problems at all. And than one workout day, a odd feel to these exercise may develop; as burning, undo stress, etc within the working triceps/elbow area.
Just to note: Highest weight I have witnessed (and confirm) in workout reps (sets of 6's) for SkullCrushers was around 320lbs, or so., but have heard of much heavier weigh used (can not confirm).. SkullCrushers are a partial rep movement, not gaining near a full stretch, still the pressure/stress on the elbows was brutal...Also commented on related potential biceps tears on injury/rehab site, which may reflect with regards to the triceps. ..two better triceps exercise that no one does is a the one arm DB kick back & the tricep push off /push back bwt movement. Good Luck..