While various definitions of "dialect" exist, they're all subjective to some degree. There's no litmus test and no comprehensive, entirely objective answer to the question of what's a dialect and what's a language.

The most rigid definition insists that while "dialects" are more or less mutually intelligible (and "languages" are not), "real" dialects exhibit differing details of syntax (grammar rules), as well as of pronunciation and vocabulary.

The traditional syntax of Scots is essentially identical to that of standard English, though there are some very minor differences that most people don't even notice. So its "precise" overall status (assuming there can be one) is moot.

In practical terms, the distinction between "language" and "dialect" is of more political than scientific interest.