"Trapped" or "To be trapped"

Question

Emergency services attended the scene and found the man trapped in his car. A crew from the State Emergency Service (SES) with the assistance of Fire and Rescue extricated the man from the vehicle before NSW Ambulance officers treated him on scene. Source

Authorities have identified the man who was trapped in his car for three days after rolling the vehicle in a remote part of Montana as 30-year-old Shaun Lee of South Carolina. Source

First of all, I have no idea while the verb is "be trapped", the to be part 'was' is missing in the first passage.

Secondly, I was wondering if using "who" is an optional part which adds to the formality of sentence in the second passage.

I.e. please do me a favor ant let me know which case below sounds correct to you and why:

There was a 4-car-pile-up on the road. I parked my car at the side of the road and went to help the man................in his car.

a. trapped
b. who was trapped

If they both work, then how they differ semantically?

Please kindly explain those to me.

Answer 1

In the first example,

Emergency services attended the scene and found the man trapped in his car

This phrasing suggests (at least to me) that at the time when the emergency services arrived, he was trapped.

The second example,

Authorities have identified the man who was trapped in his car

This phrasing suggests that the man was formerly trapped in his car, but no longer is.

In the second passage, the word 'who' is not optional, but could be replaced by 'that'. This is because the phrase "The man who was trapped" is a noun with a little extra information, but "The man was trapped" is a statement.

tldr: a and b both work perfectly fine