I know that for huge input Hash's Output is much smaller, SIG's Output is of same size, but what about MAC's Output?
The vast majority of signature schemes in use today produce constant-size signatures, irrespective of the size of message they sign. Exceptions would be signature schemes with message recovery, where the message is embedded in the signature - but those are exceedingly rare.
Similarly MAC constructions produce constant-size authentication tags, irrespective of the message size, too.
The usual way by which this is achieved for signature schemes is by use of a (cryptographic) hash function - e.g. the first step of the RSASSA-PSS signature scheme is to hash the message. For MACs there are more diverse approaches, with both cryptographic hash functions (e.g. HMAC) as well as 'truncation' of the output (e.g. CBC-MAC) coming to mind.
The difference between a MAC and a signature scheme is then twofold. Firstly the former is part of symmetric cryptography while the later is part of asymmetric (or public-key) cryptography. Secondly the formal properties they strive to achieve differ - for details on that check any standard textbook, or also the post you linked above.
I do not understand your second question:
If MAC's Output is of same size isn't there something that combines both short output and using keys for encryption (ie SIG and Hash Together?)
If there is something left unclear, please clarify what you mean by 'same size', and 'combines short output and using keys'.