"What is the difference" is the correct form.
In answer to your question, they both mean the same thing but they have a slightly difference sense.
To take a trip: implies pleasure/relaxation/leisure.
To make a trip: implies effort/necessity/work.
For example:
I must make a trip to the shops to get some butter.
I'm taking a trip to Paris to see a friend.
Hope this helps,
Take care,
Josephine