I think the difference is something like Feynman’s trick simplifies a hard integral by introducing a parameter and differentiating the whole integral, while substitution simplifies an integral by changing variables to undo the chain rule. But it has been so long since I've done integration manually I'm not 100% sure that's an accurate description/the full story.

The thing I hated about integration was which approach would work and the best option for each approach were much more "do a lot and see what's right" and I was too lazy :).