Both the situations are exactly not the same.
First of all the master-slave connectivity should have been also added at the intermediate locations (see below).
Secondly, the important part is the the difference in the lateral stiffness of the column. See the screenshot below. In case of the offset specification, the column stiffness remains same upto the entire length. The fictitious infinitely high stiff mathematical member (due to offset specification) connects the column tip and the beam end node but that does not affect the stiffness continuity in the column across its entire length.
Whereas, in case of the Master-slave specification, the column is already curtailed and the remaining portion is connected by the infinitely high stiff connector by the master-slave specification. here the actual column stiffness continues upto the beam column junction(see the illustration below) and the remaining part is considered as the infinitely high stiff and hence as the overall lateral stiffness of the entire column arrangement is relatively higher than hat of the former case and hence its corresponding lateral displacement and other reactive forces slightly varies. 