...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.»
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?"