Is the 24C the same as the 24E except for the shoe?

No, they are not the same. Here’s the main difference between the 24C & 24E, other than trigger shape.

The 24E’s initial creep is very short, some say a “hint of creep,” with subsequent shots exhibiting a little less creep if trigger let-off is stopped at hammer reset and the follow-up shot is made from there.

However, on the 24C, the initial creep is virtually zero, i.e. it creeps, but most shooters can’t feel it. And, regardless of finger control during reset, subsequent shots are identical in feel to the first shot, resulting in optimal feel consistency and trigger transparency. Trigger transparency means that the shooter now can simply think “shoot” and the rifle fires instead of being over conscious about the feel and mechanics of pulling the trigger, which is a distraction to shooting resulting in poor timing and poor accuracy. The reason no one likes MIL-spec triggers is that you can’t keep from thinking how terrible it feels. That’s not transparency.