is the former one used in any kind of trained hunting process?
Yes, in falconry.
Peregrine falcon
The peregrine falcon is a highly admired falconry bird, and has been used in falconry for more than 3,000 years, beginning with nomads in central Asia.
what is referred to as pale crag martin? A small passerine bird. from where did its name originate? The genus name is derived from the Ancient Greek "ptuon", "a fan", referring to the shape of the opened tail, and Procne , a mythological girl who was turned into a swallow. The specific name "obsoleta" means "worn" in Latin. where is it found? Northern Africa to Middle East extending up to Pakistan and Afghanistan. what are its sub-species? UNANSWERABLE any species which hunts them? Peregrine falcon, Taita falcon, African hobby and wintering Eurasian hobby. what exactly is the first one? A widespread bird of prey. and the second one? It is another type of small falcon. how does it behave? It perches for long time, emerges to prey on birds with  fast, parrot-like wingbeats. Occasionally, it soars high.
wiki:5326025
Peregrine falcon [SEP] Use in falconry
The peregrine falcon is a highly admired falconry bird, and has been used in falconry for more than 3,000 years, beginning with nomads in central Asia. Its advantages in falconry include not only its athleticism and eagerness to hunt, but an equable disposition that leads to it being one of the easier falcons to train. The peregrine falcon has the additional advantage of a natural flight style of circling above the falconer ("waiting on") for game to be flushed, and then performing an effective and exciting high-speed diving stoop to take the quarry. The speed of the stoop not only allows the falcon to catch fast flying birds, it also enhances the falcon's ability to exert maneuvers to catch highly agile prey, and allows the falcon to deliver a knock out blow with a fist-like clenched talon against game that may be much larger than itself.