My book doesn't say anything about this and leaves it ambiguous. The periodic table they gave colored the inner transition metals as "transition metals". So, are inner transition metals also part of the transition group?
Well to categorize them, you need to first define what transition elements are. One definition is etymological, that, 'the chemical properties of transition elements are transitional between those of s and p-block elements'.
A more refined IUPAC definition is that 'transition elements have an incomplete d-subshell, either in the neutral or ionic state'. The f-block elements/inner transition elements meet this criterion, so yes, they are transition metals. You can read more about it here.
The reason why they are in separate blocks is due to the reason that they have successively varying f-subshells and frankly, to accommodate the periodic table on one regular-sized page.