Welcome to this forum.
I’m not fully sure about lobha, but I will say that since taṇha and upādāna become split in dependent origination and in practice, my interpretation of that is that taṇha is like an initial passion, thirst, and craving, while upādāna is attachment and holding on. In that way, taṇha wouldn’t be attachment.
In lobhasutta, completely giving up lobha means anāgāmi, which would imply lobha is kāma taṇha (excluding bhava taṇha and vibhava taṇha), so greed is close but limiting, but that doesn’t mean it will mean exactly that everywhere else.
I think that sometimes these terms are referring to the same specific mental formations that we can find familiar, and that’s what the point of using these terms is. The term attachment is useless unless you have the awareness to know what I’m really referring to when I say that, and even then, it has many meanings. So we can’t always equate words to philosophical categorizations, especially in some verses where it might even treat each of those as the same. So you will just have to fall back on contextual guesswork, letting language run its course through you, which isn’t really an answer but not every question needs to be answered (now).
For the record there are even more terms that are similar to desire like abhijjhā and icchā.
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