Is there a real difference between "to mull something over" and "to think something over"?

Question

I've done this exercise focusing on phrasal verbs. There was a sentence, something like this:

I need to ...... it over before I make my decision.

The particle "over" gave me only two choices - mull x think, whose respective definitions are:

mull over - to think carefully about something over a period of time

think over - to consider a problem or decision carefully

The key says that the only correct answer is "think over" (at school I was prudently told that even though a textbook can be the best ever, it does not mean the key is always correct (which is an assumption that has been confirmed by this very key, in which I have already found two mistakes).

Both these words seem identical with little to no difference in their meanings. Can, possibly, native speakers see that big a difference between them that would limit their interchangeability? If you go to a car dealership and the person there tells you:

"Here´s the complete catalogue, go home and think/mull it over."

According to their definitions, both words seem perfectly correct.

Answer 1

They are not denotatively different - that is, they have the same "definition". You could use either interchangeably and be understood.

"mull over" and "think over" can connote different senses of the actor's disposition, however, and that's what those differing definitions try to express.

"Mull over": connotes a sense of thinking about in an easy or relaxed way, perhaps taking your time; no rush...

"Think over": is color-neutral. Doesn't connote anything except thinking about the thing. Use this one as a default.