As for words similar in this case, they are identical in both situations.

If we talk about previous in the future we

can say: “I think John will invite me… I think John is going to

invite me… I think…” For these predictions we can use both

“will” and “going to” Your sentences are ‘future in the past”, and in that case, “will” becomes “would”, and “is going to”

becomes “was going to”