tense - The Present Perfect Progressive and the Simple Present Perfect

I'm trying to understand the difference between these two perfect verb-forms. Could you explain the difference between the following sentences:

I've been playing a lot of tennis recently.

and

I've played tennis three times this week.

I also would like to understand, what is verb-form preferred in my first sentence:

I'm trying to understand the difference between [...]

or

I have been trying to understand [...]