Make a trip/take a trip or go on a trip?

whats the difference between these concepts?

-make a trip
-take a trip
-go on a trip

In order of use, I would say that it would be:

Take a trip, go on a trip, make a trip (almost never used unless you attach the phrase "out of it" at the end, which is very specific).

Take a trip and go on a trip are very similar.

I took a trip to mexico last week and had a good time.

I'm going on a trip to europe next month with some buddies, I am really looking forward to it. 

Make a trip isn't used or correct in my opinion. Although, the expression "make a trip out of it" is used when a group of people travel somewhere for a different purpose or reason and decide to stay longer than expected- they could say, "let's make a trip out of it."

But you will be fine with using go on a trip or take a trip interchangably.