Control and raising are distinct mechanisms for linking subject positions across clauses: raising involves NP movement to a higher clause, while control involves a null subject (PRO) in the lower clause obligatorily coreferent with a matrix argument.
Compare minimal pairs distinguishing control from raising (e.g., 'John tried to leave' vs. 'John seems to have left'), examining which tests (passivization, tough-movement) apply to each.
Both involve a coindexed subject relationship, but raising is movement (one argument), while control is composition of two separate predicates.
From your work on the Minimalist Program you know that syntactic derivations involve movement operations (Merge, Move) and that argument structure maps thematic roles onto syntactic positions. Control and raising constructions are the key test cases for understanding how matrix and embedded clauses interact — specifically, how the subject of an infinitival complement gets its interpretation and its thematic role.
Consider two sentences: *John tried to leave* and *John seems to have left*. Both look superficially similar — a matrix subject, a main verb, and an infinitival complement. But they work differently at a deep level. In *John tried to leave*, John is the agent of both trying and leaving. The infinitival complement has its own subject position, occupied by PRO — a phonologically null pronoun whose reference is controlled by (bound to) a matrix argument. This is an obligatory control construction: PRO must refer to John, not some arbitrary person. John bears two thematic roles (agent of try, agent of leave), and the sentence involves two separate predications joined by the control relation.
In *John seems to have left*, John is not an argument of *seem* at all — *seem* is a raising predicate that takes no external argument. John originates as the subject of the embedded clause (agent of leaving), and raises to the matrix subject position to satisfy the EPP (the requirement that TP have a specifier). This is why raising predicates pass the expletive test: *It seems that John left* works perfectly, substituting the expletive *it* for the raised NP. But *It tried that John left* is ungrammatical — *try* is a control verb that requires a referential agent in its subject position. The same test distinguishes raising from control across constructions: if you can substitute *it* or a non-referential expression (*There seems to be a problem* but not *There tried to be a problem*), you have a raising predicate.
The practical diagnostic toolkit matters because the distinction has real consequences for semantic interpretation. Idiom chunks provide another diagnostic: *The shit seems to have hit the fan* is grammatical because *the shit* raises from the embedded clause where the idiom is intact. *The shit tried to hit the fan* — interpreted as an idiom — is blocked, because *try* assigns a thematic role to its subject, and *the shit* cannot be an agent. Similarly, the tough-movement construction (*John is easy to please*) appears superficially like raising but actually involves a gap in the embedded complement — an A-bar movement phenomenon distinct from both control and raising. Keeping these constructions distinct requires asking, each time, where each NP receives its thematic role, and whether the matrix predicate takes that position as an argument or merely as a structural host.