"To get" simply means "receive", while "to take something" means "to put some effort into getting something". When we think of the word "take", we (or least I do) imagine reaching out, grabbing something, and pulling it back towards us. For example, if you said "I got a cake", you're not saying anything about how you got the cake. Maybe you took it from the kitchen (you walked into the kitchen and brought the cake out; although in the right context it can also mean that you stole it from the kitchen). If someone put it in front of you, you can't say you took it. "Get" and "take" are both very common words, so they both exist in a lot of phrasal verbs.

"get" es un verbo muy complicado, como tu verbo "llevar". Usamos "get"en muchas muchas maneras

I am taking a piece of cake casi lo mismo como I am getting a piece of cake. Tal vez otra persona pueda explicarte la pequena diferencia.

I am taking some clothes (from my house-pero no necesitas decirlo) to the cleaners. I am taking the children to the movies. I am getting some food from the grocery store. I am getting some advice from my sister.