permutation..confusion

in book its given that the number of ways to distribute 3 identical A's into 2 different groups ( when empty groups are allowed) is 4, which is correct....

also the no. of ways to distribute and arrange A,B,C into two different groups ( when empty groups are allowed) is 4*3!,which means that if we were asked to find the no. o f ways to distribute A,B,C into 2 different groups ( when empty groups are allowed) should be 4....

here is my confusion that if we take this into account then the no. of ways in which n identical things can be distributed into r different groups ( when empty groups are allowed) = no. of ways in which n distinct things can be distributed into r different groups ( when empty groups are allowed)

Is it correct? plz explain if its correct....