To add to BPF's comments, a "Flight Manual" requires, and will be approved by the certifying authority for the aircraft. It will probably be specified as a part of the type design or the aircraft, and must be carried for reference.
A POH, or Owner's Manual might also be a "Flight Manual", if it says so in the first few pages, and states that it is [FAA] approved. Without that reference to being approved, it is not the flight manual for the aircraft.
Demonstrating of this difference can be found for some Piper Twin Comanches, (there may be others too) where the formal looking POH is a different document from the FAA approved Flight Manual. The pilot is responsible (somehow) for knowing that there are two distinct documents.
It is important for the pilot to understand the authority of what they are referring to. If there is an approved flight manual, it will say that it is, and the pilot must refer to it. For aircraft older than the early '70's, there may not be an approved flight manual, in which case, there will be a limitations placard in view of the pilot, and that must be followed. What's in the POH or OM, is good advice, but not truly regulatory.
Also note that a particular aircraft, with certain equipment, modifications, or AD's, may have Flight Manual Supplements, which the pilot must read and follow. In some cases, failure of the pilot to read and understand the changed information can be life threatening. Examples of this I have experienced included an early model Cessna 303, fully equipped and placarded for flight into known icing, (and that's what we were doing with it at the time) which I later found upon reading a emergency AD flight manual page was prohibited any flight in icing. I was curious, as earlier in the flight, I had darned near lost control of the 'plane in icing conditions. The amended FM page explained why I had come so close to killing us both. The type was later modified to return it to FIKI no problem. Another example is some Navajos, which though able to extend 40 flap, are AD limited to 25.
But my most extreme example of getting to wrong, while piloting a 'plane with an approved Flight Manual was the "Found Bush Hawk". I was flying w brand new one on skis. 3 hrs TTSN straight from the factory. I read the entire wheel plane section of the Flight Manual. I stopped reading at the floatplane supplement, As this model of 'plane had never flown on skis before, I knew there would not be a skiplane supplement. And the supplements for the radios? I knew those already. What I missed was the fact that there was, in the very back, an FMS for the aircraft, when equipped with fowler flaps (as opposed to plain). I only found this after my flying. For reasons lost upon me, the Found company had elected to present ALL of the basic Flight Manual data again, with many subtle differences (speeds) as a supplement, rather than a new FM or the aircraft. I noted to the approving authority what a poor idea this is. The existence of the approved Flight Manual in the front of the supplements, would lead the pilot to think the for that configuration, they had the information they needed. I received an indefinite reply.
The bottom line is to read and understand what you have, and what supplements may be in the back, which are applicable to the configuration you're flying - it can make a difference!