같이 and 처럼 are both used with nouns.
Both of them express that some action or thing appears the same or very similar to the preceding noun. It corresponds to "like" or "as...as" in English.
They are nearly identical in meaning and usage.
There may be a few rare exceptions, but as a general rule of thumb, know you can use them interchangeably.
The only exception I've noticed is that 처럼 can be used with 마치, whereas 같이 cannot.
I see both used often.
Considering the origin though, 같이 is related to 같다.
같다 : to be the same, identical (to/with), equal (to), equivalent (to)
There's also 같은, 같이 meaning together, and the ability to use 같다 as a verb and in other grammar structures.
(My original answer from here: http://www.italki.com/question/300999)