The one carrying/the one who carried

Yes, you can use both. And they both have the same meaning.

no!

hehe, I´m just kidding...thank you!!!!!!!,miss Allein..

for learningwhether I could use the second sentence with the same meaning as the first one

You can use it with the same meaning or with a different meaning.

If you take the first to mean that the one who is now carrying the box was a doctor, then the second means something slightly different because it has to do with the one who carried the box

Imo,

First one is good
The second one is a little too formal.

Thank you very much!

Maybe, I shoud say:

"The man who carries the the box was a doctor", to make it similar to:

"The man carrying the box was a doctor".

I can see, from your answers, that the difference rest on the grade of formality.

Thank you , again.

for learning.