Will AES-GCM smaller sized tag (mac) be included in larger sized tag
Yes, that's what the standard mandates.

First we need to note that if you fix a key and an IV, then AES-GCM becomes fully deterministic, that is the same input will yield the same exact output.

Then we look into the standard, NIST SP800-38D (PDF), and look at the way the tag is generated.

$$T=\operatorname{MSB}_t(\operatorname{GCTR}_K(J_0,S))$$

which effectively tells us that the $t$ most significant bits of the tag output (which is the same for both invocations) are to be used for the tag.

Then we look up the semantics of the $\operatorname{MSB}_s(X)$ function which are:


  The bit string consisting of the $s$ left-most bits of the bit string $X$.