"Late to the party" vs. "late for the party"

"Late to" implies that you are present, but late enough that the "party" is already well underway. "Late for" implies that you haven't arrived yet (or have just arrived) and the "party" has started.

The respective connotations are that if you are "late to" a party, the best food and drink is gone, conversation groups and dance partners have formed which are harder to chisel into, people have already had a few drinks, and generally you have missed out on having the best time. This holds when used figuratively; a person who shows up to a sale after the item they wants is gone or the deadline has passed, or in business terms if a "late mover" enters a product market that is already in decline, they have "missed out" on getting the best deal or a good share of the revenue.

Being "late for the party" is less commonly used figuratively, but is often heard in context of a new person joining a group just before (or after) the group embarks on something: "Am I late for the party?". The connotation is that the "party" (the event in which the person wanted to participate) may or may not have begun; the speaker is asking which.

"Late to" suggests that you are not going to make it to the party on time. This also applies to other events:

Crap, I will be late to the graduation ceremony.

The focus here is that whenever you arrive, it won't be on time.

"Late for" encompasses the "late to" definition but also includes the idea that you are now at the proper location but it is so late that you missed the event entirely:

I arrived far too late for the party.

To say the earlier meaning:

I am late for the graduation ceremony.

Notice the switch from "I will be late to" into "I am late for". Technically, this is more accurate but real usage suggests that each phrase is completely interchangeable.

Arg... I am late to the party

If you don't hurry, we will be late for the party!

I believe the question here is being directed to the figurative use of the phrase. Being "late to the party" means most people became aware of something before you did, or adopted something before you did. For example:

Yesterday I set up a Facebook page. I guess I'm late to the party, hm?

In this case, it's always "to" the party, not "for."