Mono vinyl, how do you know if really single channel mono or if stereo recorded to mono

That is news to me.  If the record album says mono, I play it on my mono rig.  It sounds like you want to use your stereo cartridge on the “two channel mono” you describe.  Many albums were recorded in mono and stereo, and you can find both.  This is of course clearly labeled in most cases. Your issue is?

Actually it’s often a mono master that simulates stereo when pressed in stereo. Remember those simulated stereo when drums are in one channel and vocals are in another channel? This is how they make stereo out of mono master. This is not a true stereo record.

Regarding stereo to mono:
You can do that with one button on phono preamp (if you have mono switch).

What’s the point to make mono press out of stereo master ? Why ?

The reason labels released stereo from mono is because stereo was something new and mono masters already recorded in mono earlier.

Mono press does not have vertical modulation of the groove, only lateral. You can play it with one speaker. 

P.S. If you’re referring to stereo cutter head used to cut mono lacquer than it’s true, most of the modern mono records cut with stereo cutter head as far as I know.

State of the art mono records (made from mono master) are old, vintage. Those are true mono. If they are not pre 50’s then you can play them with modern stereo cartridge. You can also play them with true mono cartridge if you wish, but it’s not necessary to have conical tip for mono, actually advanced profile of the stylus tip is a benefit for the sound quality anyway (even for old mono, except for pre 50’s era mono with wider groove) and life span is much longer, also less record wear. Advanced stylus profile wasn’t there when mono was a standard.

It sounds like you want to use your stereo cartridge

no.. At this point I’m not wanting to do anything other than understand what is happening. As I stated in my post .... I am exploring getting a mono cartridge

What’s the point to make mono press out of stereo master ? Why ?

My question has nothing to do with converting stereo to mono. It has to do with how a mono record is made with a mono master, how the groove is cut in the vinyl... and how a cartridge "reads" that groove, , are mono records cut with stereo heads the same as those cut with mono heads, and ultimately, what kind of mono cartridge is best to get?

before stereo there was only one way mono records were made, with a mono cutting head that only moves laterally.

after stereo you can also cut a mono record with a stereo cutting head by applying the same signal to both channels. So one question is.. does this result in the same thing as using a mono cutting head i.e. only lateral motion during playback? In other words, if I used a mono cutting head to make one record and a stereo cutting head to make another from the same recording, would the grooves be identical? So I admit my initial question about how to tell the difference was not the right question, the question is, are they different?

I ask this because I don’t know if a "modern" mono recording cut with a stereo head is better off played with a stereo cartridge since it was cut with a stereo head, or does playing it with a mono cartridge offer the same advantages as playing one cut with a mono head. I ask this because there are a variety of mono cartridges, some that are actually stereo cartridges strapped to mono, and some are true mono i..e. they only have output in response to lateral motion. I ask this because I am exploring getting a mono cartridge and I’m trying to understand the differences in this variety of cartridges and which is the best kind to get. It obviously isn’t just a matter of buying a cartridge that is labeled as mono because there are different ways they are made and different stylus profiles.

thank for the responses but I obviously wasn’t very clear in my initial post so I am trying again...