I tried to understand the exact usage of these two below (How do you call this "the same"? A phrase? I tend to call any thing (?) with two or more words as a phrase eventhough they as a whole do not give out any appreciative notion. Am I right to call "the same" a phrase?) and their implications but having some difficulties.

It is the same.

It is same.
Same is a word that is (almost) always preceded by an article or determiner; in that sense, I would call the phrase highly collocated or idiomatic. Therefore, your second sentence is incorrect.
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Thank you. As you said the word "same" is (almost) always preceded by an article or determiner, can you supply me with a precious one example of the exception to the general application?
The word same is always preceded by a determiner.

'I'll have another,' she said.
'Same here,' I echoed.