How do one define acquisition range of #PLL?  What is its dependence on loop bandwidth?

How acquisition range differ for discrete PLL instead of normal PLL?

How does one define the meaning of the term, or how does one calculate a number?  The answer in both cases is "it depends", but different.  "It depends" and it's complicated -- my analog-only PLL book devotes 30 pages to acquisition.

Normally the definition of the acquisition range of a PLL is the range of frequencies of the source tone that the PLL can lock to.  Sometimes you'll turn this around and define it as the range of frequencies that the PLL oscillator can have and still lock to a steady tone.

The acquisition range can depend on loop bandwidth -- the acquisition speed certainly does.

I can't really answer your question about the difference between a discrete-time PLL and a "normal" (presumably continuous-time) PLL because there are too many different ways to realize a PLL within each of those broad categories.  Again, in the PLL book that's at my elbow right now, there's 30 pages devoted to acquisition, and they occur 155 pages into the book -- and you need to have understood most of those 155 pages before you can really appreciate the chapter on acquisition.

If you have a specific PLL topology in mind, or if you have a specific problem to solve and you want help, post a question.  Otherwise, if you need to know this PLL stuff then ask for a book recommendation (or, if you have that luxury, take a class).