To think we are in a relationship?

Well actually he couldn't

There would be at least the administrative burden of divorce, CMS, financial arrangements and the like if you were married with three kids.

Currently he could walk away in the next ten minutes with no need for any discussion beyond 'I'm done' - that's the freedom that his position of 'not being in a relationship' gives him

What’s interesting is that OP said he’d changed after she had another relationship. She’s not said how he’s changed but we can make guesses as to how. Maybe he changed so he could be with her but sort of on his/her terms, keep her sweet if you will. It probably wounded his pride that she had another relationship as he wasn’t expecting that.

Well he doesn’t need to commit, share bills, finances or anything like that.

OP, being a non-cohabiting boyfriend is about the lowest level of commitment you can get yet he won't even call himself that. Ffs. Wake up.

As low a level as it is, here's what it entails:
Public acknowledgement of the nature of your relationship. None of exist in a vacuum, this is important.
If he has sex with another woman, he will get grief from you, his family and possibly his friends.

Giving up sexual opportunities with other women. This is no small thing for a guy.

Basically, he is not that into you as he would (at least for a while) risk public opprobrium if he treated you badly or give up sexual opportunities.

I think that - rightly or wrongly- you percieve yourself as far less attractive than he is.
Am I right?

Above all, remember one thing:
no label=no relationship=no rules

After several hundred messages and lots of sensible opinions, I find your responses rather defensive and fixed. If he is so perfect and you are not bothered either way, and you are so sure he is 100% in to you / faithful to you / committed to you, then why have you felt the need to post?
I suspect the truth is that on some level, you do feel insecure about the fact he refuses to be in a 'relationship' with you, and you are wondering what else you need to do /be to convince him. His refusal to name all that you are to each other, all the time you spend together as a 'relationship', feels on one level slightly insulting.
I'm sure you will come back and say this is not true... But I would ask you to dig deep and ask why you felt the need to muse on this particular subject. Its completely reasonable to want acknowledgement of your place in his life, after several years, it seems churlish that he won't call you his girlfriend / partner.
Personally, I think I would bin him off over this, but you may feel differently

Saw a video today that described a man as a taxi, if his unavailable light is on he isn’t interested. He has to chose you, you can’t chose enough for both of ye. Carry on as you are OP but if he died you wouldn’t be chief mourner or next of kin. That matters when you love someone and they love you.

Oh OP, I feel for you, I have been there

A smart woman would not settle for less that she wants, that’s the bar between smart and stupid.

You want a relationship. That’s your dream, it effing matters. You should cherish, respect and care for this dream, rather than let it get it rubbished (and your life with it) because you met a “halfway there” (some guy with some qualities but also some crucial stuff missing).

Your chance of getting what you want out of him are pretty low. Your chances of getting another great relationship with the commitment you want are unknown, but if I were you, I d take my chances anyway, the odds are very probably much better.

I hope you start to unpack why you want to ignore your dream for just another bloke, why you treat yourself and your own wants with such disregard. Why it has to be him and not one of the billions of other blokes currently roaming the earth. Why you try to pretzel your brain into some weird reasoning to make it acceptable, like this thread.

You want a committed relationship. He doesn’t offer that, then he’s not for you, he’s not worth staying in your life. That’s all the logic you need.

The difference is in calling it a relationship or not, you're right, and that view/attitude is in itself an important difference. A man who is proud to call you his girlfriend and is eager to see himself as part of a couple has a very different attitude and value system than a man who wants to keep you at a certain distance and doesn't want to be in a relationship.

Both men may be in love, but the first man has a healthy attachment system and the second either has some childhood trauma or is very immature (or simply doesn't care that much, but you say that's not the case). The first man is more conventional/traditional, the second more a free spirit type. The first man sees a romantic relationship as something positive that adds to his life, the second sees it as something to be avoided.

What's in a name? A lot.

He's got all the benefits of a girlfriend, without the commitment of being in a relationship. This makes you a placeholder. A placeholder that he treats well, but a placeholder nonetheless.

When he meets someone who blows his socks off, he'll walk away, dropping you like a hot potato. You will cry, and say, 'but we were making plans for the years to come!' And he will look at you as though you are being crazy, and he will say, 'but I always told you we were not in a relationship!'

You will be left wondering how he could throw you away so carelessly, and no-one else will understand why you feel betrayed, because he always said you weren't in a relationship.

Could you ask him to explain how he would describe you to his friends/family? Friend, girlfriend, partner etc. That might be useful.

@Beingaboutare you just being obtuse for the sake of it now?

You asked for opinions, people gave them in droves, the majority of which disagree with you.

You either in a situation where nothing anyone says will change your mind, in which case posting was pointless or you know the answer to your own question and you’re just carrying this on now

There is a massive difference, particularly in attitude. But clearly you don't want to hear that.

So he’s changed since you’ve been back?

I think he has the freedom that as he states he’s not in a relationship he can (I’m assuming) behave as a single man.

You identify as being in a relationship.

One of the key determining factors is mutual agreement that you are in a relationship.

You wish you were, feel like you are, tell yourself you are but it's not possible to be in a relationship with someone who doesn't want to be.