Recover, regain, retrieve, recoup, recruit can mean to get back something that has been let go or lost.
Recover, the most comprehensive of these terms, may imply a finding or obtaining something material or immaterial that has been lost or a getting of something in reparation or compensation.
Regain, though often used interchangeably with recover, carries a stronger implication of winning back or getting once more into one’s possession something of which one has been deprived.
Regain also may imply, as recover seldom implies, success in reaching again a place or point at which one has been before.
Retrieve implies a recovering or regaining after assiduous effort or search.
But retrieve sometimes takes for its object such words as loss, error, failure, or disaster, then implying not recovery but a setting right or a making what is bad good, or a reparation by making up for what was wrong or unsuccessful.
Recoup, basically a legal term implying a rightful deduction by a defendant of part of a claim awarded to a successful plaintiff in a lawsuit, can in its general and extended use imply recovery or retrieval, usually in equivalent rather than identical form, of something lost.
Recruit fundamentally implies growth through fresh additions; in military use it can imply an increase in numbers through drafting and enlisting or a filling of vacancies in a force resulting from casualties.
In more general use it may imply a regaining of what has been lost (as vigor through illness, or money through extravagance or heavy expenditures) by fresh additions or replenishment of the supply.