Is my cat making friends or enemies with the neighbour's cat?

Unlike dogs, cats don't roll onto their backs as a sign of submission. It's usually the position of the more aggressive cat because it means they have all 4 sets of claws and teeth ready to defend themselves. It enables them to grasp their opponent with their front paws whilst kicking hell out of them with their powerful back legs, giving them a distinct advantage over the other cat.

In the cat world height means status, so they will stand over a rival or raise their paw over their head to assert dominance. A submissive cat will cower or flatten themselves as close to the ground as possible but they won't want to expose their belly because that's their most vulnerable when it comes to injury.

You know these 2 cats better than us, but it does sound as though your cat is prepared to stand up for herself. If you didn't have a cat before, your garden would have been unclaimed territory and perhaps the neighbour's tom considered it his. He may have decided to show this "intruder" it was already claimed, but then thought better of it when she didn't back down from his posturing. I think a few more showdowns are inevitable until she has established her claim to the garden. Continue to accompany her outside so that you can keep an eye on them and intervene if necessary.

They probably won't ever become friends, but they will learn to tolerate each other and work out a time-share arrangement over the local gardens. The recent BBC documentary "The secret life of the cat" showed that time-share arrangements are how cats in the same neighbourhood avoid conflict and fights.

First the fact that Buddy isn't neutered is very unsettling to Bell. Those hormones smell very threatening to her. And not all cats like all other cats. Do you like every person? Cats are no different. He is invading Bell's territory and that is very upsetting to her. I'd keep Buddy out of the house - for two reasons. One, he's an unneutered cat which means he fights other Toms and can pick up diseases like FeLV and FIV. FeLV is very contagious, and you are risking Bell's health by allowing them contact. And two, if Bell gets fed up enough with his coming into HER home and HER territory, she's going to express that by urine marking in her house. They are NOT going to be friends - and she is not just being rude. She's being a cat, and is trying to tell you that she does not like this smelly male cat hanging around.

Intact males are not interested in making friends, they are only interested in mating and driving off intruders in their territory. Since your cat is useless for the first purpose, he's going to attack her as long as she is invading what he perceives to be his territory. Unless you want her hurt, you need to keep her indoors and away from him. It's a genuine fight, and she will probably end up on the losing end.

This is serious fighting, where the cats will get hurt. You shouldn't be letting your cat outside anyway.

She obviously hates that cat keep her away from him