To my knowledge, the first sentence is a simple event of the past, and it has nothing to do with the present. That's it.
No facts are given to the state of the present.
If by this you mean the car has been recovered or that this is a long distant past where the speaker no longer cares or isn't so concerned about the missing car, then no, that's not true.
For the same event, native speakers of English have a choice of the Present Perfect aspect [PrP] or the simple past tense. For NaE speakers, the PrP is reserved more for past events that the speaker wants to make relevant to now. This includes HOT TOPICS.
News outlets often make use of the PrP to make the new more NOW, more current, more interesting.
On the other hand, the second one is a combination of the past and the present.
That is true.
The car was stolen in the past, and at the same time, it suggests that obviously the speaker doesn't have the car now. That is, the second sentence implies both of these.
That is possible but it is NOT always the case. It could be a PrP of experience,
"My car has been stolen",
meaning, sometime in my life, a car of mine has been taken, but that could have happened forty years ago and the car was quickly recovered but I no longer have that car - it may even have gone to the wreckers.
You just have to understand that English has this PrP aspect and understand the reasons English speakers use it. Then to become proficient at using it, practice using it like we do.
I'll comment on some BrE versus NaE in another post.