{I've been reading} vs {I'm reading} (present progressive vs p. perfect progressive)

Question

I think both

I've been reading that book (lately)

and

I'm reading that book (this week)

are correct. But I struggle to find a difference in meaning. Is there one? Should I avoid one tense or the other?

EDIT: I know how the present-progressive is usually used, but it can also be used for things that are not currently happening. That's the point of the question.

Answer 1

1. present perfect continuous
   for an action that began in the past and continues up to the present.

   I've been reading that book = I started reading it and I don't still finish.

2. present continuous
   • for an action happening now. (Around the present.)

     I'm reading that book = This is what I'm doing right now.

   • for something temporarily happening not necessarily at the moment of speaking.

     I'm reading that book in the evenings.

   • for arrangements in the future.

     I'm reading that book next monday.

Answer 2

Let's break apart the contractions:

I've been reading that book (lately)

means

I have been reading that book (lately).

have been reading is present perfect progressive. It emphasizes that you have been performing a continual action at a present time (lately).

I'm reading that book (this week)

means

I am reading that book (this week).

am reading is present progressive. This tense refers to a continual action that is currently occurring ("this week").

Edit:

Of the two tenses, present progressive tends to be more immediate than present perfect progressive.