You're right, there are circumstance where aru/iru can be translated in both ways. However in the literal sense these words are much closer to the "there is" phrase. If you compare "have" in English, we actually have 2 "have"s, one for general existence and one for possession/ownership/physically carried. . In Japanese, this "possession" have is expressed by the verb "motsu/mochimasu". For example, if I say "Omocha ga arimasu" implies I might not be the owner of the toy, but it still exists with me. Pets aren't really something you possess, rather they exist alongside you, so you use "iru/imasu". Incidentally you can also used the verb "to raise", as in raise a cat in the same way you'd raise a child, though I can't remember what the Japanese word is. In terms of the party, they aren't something that can be possessed either, or taken ownership of or can be physically carried etc. Rather it just exists under specific circumstances, those circumstances being "tomorrow", or if you wanted to add something like "kanojo wa" it would be like saying "under the circumstances of her, there is a party tomorrow" and thus to English it back up "she's having a party tomorrow". Hope this helps. :)