Learn English – “They are the same” vs “they are same”. Which one should be used

From American Heritage Dictionary 4th Ed. Usage Note: The expressions same and the same are sometimes used in place of pronouns such as it or one, as in When you have filled out the form, please remit same to this office. As this example suggests, the usage is associated chiefly with business and legal language, and some critics have suggested that it should be reserved for such contexts. But though the usage often does sound stilted, it occurs with some frequency in informal writing, particularly in the phrase lack of same, as in It is a question of money, or lack of same.

From Webster's Dictionary of English Usage The use of same as a pronoun, often with the, has attracted criticism from many commentators, dating back to Vizetelly 1906. The use of same as a substitute for it, this, that, and them is typically described as unliterary business jargon, if not as an out-and-out error. But a look at the long history and current use of the pronoun same shows clearly that the judgment of the critics is undeservedly harsh. Same has been in continuous use as a pronoun since the 14th century.

From Garner's Modern American Usage 3rd Ed. As a Pronoun. This usage, commonly exemplified in the phrase acknowledging same, is a primary symptom of legalese. H.W. Fowler wrote trenchantly that it “is avoided by all who have any skill in writing” and that those who use it seem bent on giving the worst possible impression of themselves. The words it, them, and the noun itself are words that come naturally to us all; same or the same is an unnatural expression.... As these examples illustrate, the phrase is rendered sometimes with the definite article, sometimes without.

So, it appears that when same is an adjective, it's almost invariably put with the. When same is a pronoun, it depends.