For a blocking operation, all four stages are combined in a single blocking procedure call.

For a nonblocking operation, the initialization and starting stages are combined into a single nonblocking procedure call and the completion and freeing stages are done with a separate single procedure call, which can be blocking or nonblocking.

A procedure is local if it returns control to the calling MPI process based only on the state of the local MPI process that invoked it.

A procedure is non-local if its return may require the execution of some MPI procedure on another MPI process. Such a procedure may require communication occurring with another MPI process.

Advice to users. Note that for communication-related procedures, in most cases nonblocking procedures are local and blocking procedures are non-local. Exceptions are noted where such procedures are defined. 

  In many cases, in the procedure name​, the additional letter "I" as an abbreviation of the word "incomplete" marks nonblocking procedures and/or as an abbreviation of the word "immediately", it marks local procedures. (End of advice to users.)

Additionally as a third orthogonal aspect, a procedure can be either collective or not.

.....

MPI-3.1 Section 3.7.3, MPI_REQUEST_FREE, page 55, lines 16-18 read

Mark the request object for deallocation and set request to MPI_REQUEST_NULL. An ongoing communication that is associated with the request will be allowed to complete. The request will be deallocated only after its completion.

but should read

Mark the request object for deallocation and set request to MPI_REQUEST_NULL. [An] Ongoing communication that is associated with the request will be allowed to [complete] continue until it is finished. The request will be deallocated only after its [completion] associated communication has finished.

MPI-3.1 Section 3.8.1, MPI_IPROBE, page 65, after lines 20-22

MPI_IPROBE is a local procedure since it does not depend on MPI calls in other MPI processes. According to the definitions in Section 2.4 with respect to the status output argument as resource, it is a blocking procedure although it returns immediately.

Advice to users. This is one of the exceptions in which a blocking procedure is local. (End of advice to users.)

MPI-3.1 Section 3.8.2, MPI_IMPROBE, page 68, after lines 30-31

In addition, it returns in message a handle to the matched message. Otherwise, the call returns flag = false, and leaves status and message undefined.

MPI_IMPROBE is a local procedure. According to the definitions in Section 2.4 and in contrast to MPI_IPROBE, it is a nonblocking procedure because it is the initialization of a matched receive operation.

mpi32-report-ticket25-barcelona-vote-sep2018.pdf 

MPI-3.1 Section 13.4.5 Split Collective Data Access Routines, page 528, after lines 20-24

- An implementation is free to implement any split collective data access routine using the corresponding blocking collective routine when either the begin call (e.g., MPI_FILE_READ_ALL_BEGIN) or the end call (e.g., MPI_FILE_READ_ALL_END) is issued. The begin and end calls are provided to allow the user and MPI implementation to optimize the collective Operation.

According to the definitions in Section 2.4, the begin procedures are nonblocking. They are also non-local procedures because they may or may not return before they are called in all MPI processes of the process group.

Advice to users. This is one of the exceptions in which nonblocking procedures are non-local. (End of advice to users.)