Today, I saw a sentence as follows: "Ein Mann und seine Frau sind bei Freunden zum Essen eingeladen". I thought that instead, the sentence should have been: "Ein Mann und seine Frau werden bei Freunden zum Essen eingeladen".
Both are correct sentences, but there's a difference in meaning.
The form "sind eingeladen" is called Zustandspassiv (passive of state), and you can find a lot about that by searching for that word on German SE. The form "werden eingeladen" is called Vorgangspassiv (passive of operation or process).
The difference is that Zustandspassiv ("jemand ist eingeladen") doesn't talk about the action or process of inviting someone, but it describes more of a quality or state. The word "eingeladen" is more like an adjective or attribute here.
"Sie werden eingeladen" talks about an action. It reports the process of someone inviting them (but from their perspective).
"Sie sind eingeladen" talks about a state. It talks about someone being on the list of invitees.
Most learning materials state that German has two passive voices.
One with the auxiliary werden that is usually called Vorgangspassiv. It's for actions that are carried out on the subject. The other uses the auxiliary sein and it's usually called Zustandspassiv. It's for telling the state of the subject after the action has been carried out.
However, there's another way you can understand both constructions. And some more as well.
For that, you have to understand that the Partizip II is like an adjective. It tells a property. Just the same as an adjective does. And it's used the very same way as an adjective. You can see this easily in phrases as this one:
die eingeladenen Gäste — the invited guests
That was the attributive use of adjectives. But there's also a predicative use of adjectives. That's when you assign a property to the subject:
Die Gäste sind lustig. — The guests are funny.
Let's vary the copula verb. You can also say
Die Gäste werden lustig. — The guests get funny.
After a few glasses of champagne, most likely. There's more copula verbs:
Die Gäste bleiben lustig. — The guests stay funny.
We switched to booze, obviously. How about
Die Gäste gelten als lustig. — The guests count as funny.
Okay, they are not funny any more. — There are even more copula verbs.
The point about those examples is that you may use a Partizip II instead of the adjective:
Die Gäste sind eingeladen. — The guests are invited.
Die Gäste werden eingeladen. — The guests get invited.
Die Gäste bleiben eingeladen. — The guests stay invited.
Die Gäste gelten als eingeladen. — The guests count as invited.
Knowing this, you may argue that German does not have a passive voice at all. It's all those predicative phrases that assign a property to the subject in slightly different ways.
The sentence with "sind" has a different purpose than the sentence with "werden":
Ein Mann und seine Frau sind bei Freunden zum Essen eingeladen
The invitation is done already. The sentence let the reader know that they are invited.
Ein Mann und seine Frau werden bei Freunden zum Essen eingeladen
The invitation is ongoing.