§61.56 Flight Review
(a) Except as provided in paragraphs (b) and (f) of this section, a flight review consists of a minimum of 1 hour of flight training and 1 hour of ground training. The review must include:
(b) Glider pilots may substitute a minimum of three instructional flights in a glider, each of which includes a flight to traffic pattern altitude, in lieu of the 1 hour of flight training required in paragraph (a) of this section.
(c) Except as provided in paragraphs (d), (e), and (g) of this section, no person may act as pilot in command of an aircraft unless, since the beginning of the 24th calendar month before the month in which that pilot acts as pilot in command, that person has—
(1) Accomplished a flight review given in an aircraft for which that pilot is rated by an authorized instructor and
(2) A logbook endorsed from an authorized instructor who gave the review certifying that the person has satisfactorily completed the review.
(d) A person who has, within the period specified in paragraph (c) of this section, passed any of the following need not accomplish the flight review required by this section:
(1) A pilot proficiency check or practical test conducted by an examiner, an approved pilot check airman, or a U.S. Armed Force, for a pilot certificate, rating, or operating privilege.
(2) A practical test conducted by an examiner for the issuance of a flight instructor certificate, an additional rating on a flight instructor certificate, renewal of a flight instructor certificate, or reinstatement of a flight instructor certificate.
§135.293 Initial and recurrent pilot testing requirements.
(b) No certificate holder may use a pilot, nor may any person serve as a pilot, in any aircraft unless, since the beginning of the 12th calendar month before that service, that pilot has passed a competency check given by the Administrator or an authorized check pilot...
§135.297 Pilot in command: Instrument proficiency check requirements.
(a) No certificate holder may use a pilot, nor may any person serve, as a pilot in command of an aircraft under IFR unless, since the beginning of the 6th calendar month before that service, that pilot has passed an instrument proficiency check under this section administered by the Administrator or an authorized check pilot.
Flight reviews are for PIC rated pilots as stated in 61.56(c). First officers do not need a current flight review to provide SIC duties on airplanes they are qualified for under 61.55. For 135 operations, they need a competency check every 12 months.
A competency check (135.293) is different than a proficiency check and it does not constitute as a substitute for a flight review under 61.56(d)(1).
An instrument proficiency check (135.297) does count as a flight review under 61.56(d)(1).
The checkride for a SIC and PIC under 135 are different. If you are curious, you can find the minimum requirements for a SIC check in FAA order 8900.
Update to answer comments
Definition of competence
adequacy; possession of required skill, knowledge, qualification, or capacity Dictionary.com
the ability to do something successfully or efficiently. Bing
Definition of proficiency
the state of being proficient; skill; expertness: Dictionary
a high degree of competence or skill; expertise. Bing
The FARs do not define these terms and so common definitions are used. As of June 2021, there are 10 references to competency check and 45 references to proficiency check. There are no legal interpretations concerning flight reviews and competency checks or proficiency checks.
If the terms "competency" and "proficiency" are synonymous as suggested in the comments, there would be no reason for this verbiage in 61.55. The authors would have simply stated one term for 91k, 121, 125 and 135 instead or purposely separating out the parts for each check.
61.55 Second-in-command qualifications
(j) When an applicant for an initial second-in-command qualification for a particular type of aircraft receives all the training in a flight simulator, that applicant must satisfactorily complete one takeoff and one landing in an aircraft of the same type for which the qualification is sought. This requirement does not apply to an applicant who completes a proficiency check under part 121 or competency check under subpart K, part 91, part 125, or part 135 for the particular type of aircraft.
The only time a SIC and proficiency check are together in the FARs in is Part 121 and I am curious if that change was due to the 1,500 hr rule for airline pilot hiring.
All the other proficiency checks in the other parts are for pilot in commands. Competency checks are used for privileges as in 61.31 (e) and 61.31(f) as well a SIC competency checks for 91K, 125, and 135..
61.157(f). Flight Proficiency for ATP candidates a candidate can receive an ATP certificate after completing both a competency check and a proficiency check. Again proficiency for pilot in commands.
All of this logically leads to one conclusion. The authors of the FARs purposely differentiated between the terms competency and proficiency. They also purposely left out the term "competency" as a exception to the flight review requirements in 61.55(d)(1).
To further prove the point. A practical test for a certificate or rating requires both proficiency and competency. §61.43(a)(3).
Competency is a minimum standard to do a job. Proficiency is a much higher standard. I would prefer my doctor to be proficient instead of competent before he operates on me. Just saying.