For an example when the practitioner wants every being to become free from sorrow, does it actually create a difference? At least when the practitioner concentrates on someone close to himself/herself. All answers are welcome and it's better if references from Pali Canon can be made.
I don't think it'd make other beings become "free" from sorrow, but it could bring certain level of peace to both the practitioner and the people s/he's interacting with. AN 11.16 mentions 11 benefits of cultivating metta:
"Monks, for one whose awareness-release through good will is cultivated, developed, pursued, handed the reins and taken as a basis, given a grounding, steadied, consolidated, and well-undertaken, eleven benefits can be expected. Which eleven?
"One sleeps easily, wakes easily, dreams no evil dreams. One is dear to human beings, dear to non-human beings. The devas protect one. Neither fire, poison, nor weapons can touch one. One's mind gains concentration quickly. One's complexion is bright. One dies unconfused and — if penetrating no higher — is headed for the Brahma worlds."
I don't know of a sutta that suggests that prayers or concentration directly affects the well being of beings being prayed to or concentrated on.
Quite the contrary, suttas like the one below suggests that such thing would be wishful thinking. That is, wishing someone to be free from sorrow as the method to make them free from sorrow is a fruitless method.
“Suppose, bhikkhus there was a hen with eight, ten, or twelve eggs that she had not covered, incubated, and nurtured properly. Even though such a wish as this might arise in her: ‘Oh, that my chicks might pierce their shells with the points of their claws and beaks and hatch safely!’ yet the chicks are incapable of piercing their shells with the points of their claws and beaks and hatching safely. For what reason? Because that hen with eight, ten, or twelve eggs had not covered, incubated, and nurtured them properly.
“So too, bhikkhus, when a bhikkhu does not dwell devoted to development, even though such a wish as this might arise in him: ‘Oh, that my mind might be liberated from the taints by nonclinging! ’ yet his mind is not liberated from the taints by nonclinging. For what reason? It should be said: because of nondevelopment. Because of not developing what? Because of not developing … the Noble Eightfold Path.
-- SN 22.101