Yes, many many songs use the same progressions. It’d be impossible to create ones “just for your song”. But that’s why melody exists. It’s the melody that’s unique. Let’s say I play the chords Am, F, C, G. As an example, Red Hot Chili Peppers songs “Otherside” and “Don’t Forget Me” both use that progression. But the songs don’t sound the same (even though it’s the same band) because the singer creates a melody over the chords.
Edit: melody isn’t strictly for the singer, the guitarist and bassist can, and do make melody. It’s just that the most common thing people know from a song, is its words, because of the strong, unique melody singers make their words flow in over the chord progression.
Latest Answers