Distinguishing between "invite" (as a noun) and "invitation" (also as a noun).
A few minutes ago, I mentioned having used "an invite" to join Tildes.
As soon as the words left my lips, I realized something interesting about the word "invite" being used as a noun.
While most people would probably assume that "an invite" was verbal shorthand for "an invitation," that doesn't seem to be the case. In fact, the two terms actually appear to have discrete (albeit related) meanings that haven't officially been codified yet: An "invitation" is either an action taken to welcome someone or a means of offering that welcome (like a physical card or a verbal statement), whereas an "invite" is a means of accessing an area to which one has been invited. This distinction is most apparent in digital environments, where one might require an access code or a link in order to enter a given site.
Think of it like the difference between asking someone to come into your house and providing them with a key. The former would be an invitation, whereas the latter would be an invite... or at least, as close to an invite as one can get without straining the metaphor. Furthermore, an invite will always include an invitation (even if it's a tacit one), whereas an invitation won't necessarily include an invite.
This is one of those cases wherein the phrase "Language evolves!" actually applies, because using the word "invite" as a noun (with the above definition) meets all of the necessary criteria for correctness: It doesn't violate any existing conventions, it adds complexity or clarity, and it arises from previously codified structures. As such, well... the next time folks are provided with invites, they can use them as part of their invitations.
What you claim invite stands for that is the part of the continued meaning of invitation.
Also, especially if it isn't codified, yet, you need to source your claims and reasoning.
The only evolving part I see is that invite might eventually ascend from its colloquial status due to its popularity.
I don't think I'd understand a difference between "I have an invite to ~" and " I have an invitation to ~" Couldn't both either be that I've been invited or that I can invite someone else?
Saying " I've been invited to ~" and "Do you want an invitation to ~" or "I can invite someone to ~" would avoid possible misunderstandings.
Here, try this:
"Hey, guess what! Someone invited me to join an exclusive online community!"
"That's... nice, I guess? They just gave you an invitation?"
"Yep! Now I'm just waiting for an invite."
"Jeez, it's really that exclusive, is it? Do they give out many invites?"
"Not nearly as many as they do invitations, unfortunately."
"That seems a bit rude. Why would you give someone an invitation if you couldn't also give them an invite?"
"Hey, at least they thought to invite me, right?"
A sentence like "Do you want an invitation to the party?" would – if we accept the stipulations outlined in my original comment – possibly be something of a tautology, depending on who was offering it.
"Hey, I'm having this little get-together this weekend. Do you want an invitation?"
"... Doesn't that question count as one?"
"Oh, I see your confusion. No, I had these little cards printed. Would you like one?"
"No, thanks, I'm going to be having an unexpected emergency that day."
Now, compare that usage to this one:
"Ugh, I can't believe Clara is throwing a party this weekend!"
"You seem awfully upset about that. Why is it such a big deal?"
"She didn't even bother to ask if I wanted to come!"
"Did you want an invitation to Clara's party? I thought you were avoiding her after... you know."
"Look, just because I don't want to go doesn't mean that I don't want to be invited!"
"I'm going to go somewhere else now."
In short, someone could invite you somewhere, but that wouldn't necessarily imply that you'd received an invite; only that you'd received an invitation.
I don't see the difference in usage between the two, honestly. If I got an email inviting me to join an online site, I would refer to that as an invite, or as an invitation. They seem completely interchangeable to me.
None of this makes sense to me. They're the same word with the same meaning... The only difference is that invitation cannot be a verb like invite can.