Q:

"past continuous tense" vs "would + infinitive"

First example:

Maria thought John was going to invite her to the party.
Mary thought John would invite her to the party.

Second example:

They thought the film was going to start at 8:00.
They thought the film would start at 8:00.

What is the difference in meaning between the "past continuous tense" and the structure "would + infinitive" when we are talking about past expectations and beliefs using the verb "think"?

A:

Although seemingly synonimous, these two uses can have different meanings.
In your examples, the first sentence expresses planning while the second one shows a general expectation/ promise.
First example:

Mary thought John was going to invite her to the party -> She thought he planned to invite her; she was on his guest list.

Mary thought John would invite her to the party -> She saw it as a logical, reasonable expectation that he did. expectation/ promise ( because they are good friends or because he said he would)

Second example:

They thought the film was going to start at 8:00.-> They thought the film was scheduled to start at eight. - plan
They thought the film would start at 8:00.-> They were told/they assumed that that was the time it started. - expectation/promise

Check some more examples and explanation of future in the past in this page
if you like. It's no grand authority as such, but there is some helpful information.

