Both ideologies goals are a moneyless, classless society, and eventual dissolving of a state government. They just disagree on how to get there, which is a huge oversimplification. But not as big as an oversimplification as what you just described. I think you should try reading the literature on it dude.

Whilst many anarchists are in favour of abolishing private property, that's not the same as abolishing personal property. I've seen a few different definitions of those two terms, but one of the simpler ways to think about it is that private property tends to be the "capital" part of capitalism.

In your watch example, if there were more people wanting a watch than watches being made, then it might make sense to first ask who has need of a new watch, and who simply wants one. There's no reason why people who want a new watch can't have one — they might just have to wait a bit longer. Perhaps another answer might be to ask whether you have any skills or tools that would be useful in making more watches, if they are in high demand. Even if not, there would likely be things you could do to help out the people making watches that could help them to boost capacity — helping out with some of their domestic labour, for example. I don't see this as being a scenario where you directly trade your labour for a watch, but rather helping to fill a niche in your community (though I do think that it would be reasonable to expect that helping out would lead to you getting a watch quicker than you wanted). That's just my take on this hypothetical though, and I'm just one anarchist.

Though it's important to clarify that whilst a communist system would be more structured than an anarchist one, anarchism doesn't involve a complete lack of rules or structures. I think that one of the reasons why this misconception is so common is because anarchism, as an ideology or political philosophy, is far more diverse and scattered than communist theory, but the development of the theory is distinct from what the development of society under that theory would look like. For instance, if we were ever at a point where we were operating under anarchism, I'd imagine that the intellectual tradition of anarchism would look quite different to what it does now — I imagine there'd be a lot of consolidation of ideas, for example.

But if you were right and you were the only person who was willing to wait until tomorrow, then all that would mean is that we'd have to figure out how to manage the demand. I don't see that as being a problem really, and more just an innate facet of life, because as you highlight, there's always going to be times when the available resources are less than the demand. A real world example that is coming to mind is a local housing co-op near me that's always got more interest than availability. They have rules about what is required for someone to get a place on the waiting list, as well as guidelines that they use to prioritise people within that waiting list. To me, this is a small slice of what anarchism could look like in practice, in this particular context — whilst they obviously are beholden to the law, the actual rules that make up the bulk of their governance are decided on and managed by the co-op.

Though for what it's worth, if you did hold off on getting a watch out of consideration for others who wanted one, I wouldn't call that being a sucker — I'd call it being a good citizen. For me, anarchism is about asking the question of "okay, what would it take for there to be more people who are able and willing to be a good citizen?". We're so far away from that level that it's hard to imagine what an anarchist world could look like, but I don't have a problem with that when there are so many examples of regular, everyday anarchism that is already working well that I can try to understand and work towards in different contexts

If the state does not wither away and instead grows into a dense jungle, you have rolled a 1 on your communism check.