A better word for that would be «trouxe» from the verb «trazer» = "to bring."
I think it should also be accepted, depending on the context.
- Você não está com frio, filha?
- Sim, mas meu marido pegou o casaco e vai me trazer.
...kinda, it is halfway there. In other words, «pegar» = "to pick (up)." In «Ele pegou no meu casaco.», that means he just grabbed it and lifted it up. «Ele, com tanta pressa, pegou no meu casaco e foi-se embora com ele.» = "He, in such a hurry, picked up my jacket and left [literally, went away] with it.»
De nada. It is hard to translate some words, when you understand the concept. :D
Can someone explain to me what is the difference between the two pharses? He took my coat. He has taken my coat.
- past tense. It happened some time in the past. This is "absolute."
- present perfect. It is used for action which began in the past but which continues into the present or has an effect which still continues. This is "relative."
I cannot really explain it too well. Most English speakers have difficulty pinpointing the difference between the two as well. Here is something I found: http://www.edufind.com/english-grammar/present-perfect-vs-simple-past/.
P.S. "Can someone explain to me what is the difference between the two phrases?"
What is then the best way to say: "He took off my coat". For example when you come in and the host takes off your coat. Is it "Ele tirou meu casaco"?