Q1- What is the total number of ways of selecting at least one object from $2$ sets of $12$ different objects, each set contains $6$ objects?
The answer is $4095$.
Q2- What is the total number of ways of selecting at least one object from $2$ different sets, each set containing $6$ identical objects?
The answer is $48$.
The difference is that in the first question the objects in a set are different, so it matters not only how many you take, but which ones. In the second question the objects in each set are the same, so all that matters is how many you take.