SelectNotFree2[expr, a, b, ...] is similar to SelectNotFree but it also differs from the latter in several respects.
If expr is a list, SelectNotFree2 behaves exactly the same way as SelectNotFree.
If expr is not a list, SelectNotFree2 first expands the expression w.r.t. the arguments via Expand2.
Furthermore, SelectNotFree2[a,b] returns 0. This differs from the behavior of SelectFree but is consistent with the naive expectations when applying the function to a sum of terms.
Overview, FreeQ2, SelectFree, SelectNotFree, SelectFree2.
Note the difference between SelectNotFree and SelectNotFree2
SelectNotFree[(a + b) c, b]a+b
SelectNotFree2[(a + b) c, b]b c
SelectNotFree[a, b]1
SelectNotFree2[a, b]0
Here the behavior is identical
SelectNotFree[a, a]a
SelectNotFree2[a, a]a
When there are hidden zeros, SelectNotFree2 obviously works better
SelectNotFree[(a - b + c)^2 - (a^2 - 2 a b + 2 a c + b^2 - 2 b c + c^2), a]-a^2+(a-b+c)^2+2 a b-2 a c
SelectNotFree2[(a - b + c)^2 - (a^2 - 2 a b + 2 a c + b^2 - 2 b c + c^2), a]0