ScottishEnglish is the umbrella term given to the various dialects of English found in Scotland as well as the generic term for "Standard English with a Scottish accent and a few Scottishisms."
There is much fuzzy overlap between ''Scottish English'' and ''Scots'', which is either a distinct language very closely related to English, or a dialect of English. (In linguistics, the dividing line between "dialect" and "separate language" is... well, ''isn't'', really, giving rise to the joke that a language is a dialect with an army and a navy.). It is possible that should English orthography be revised and removed from 16th century norms, Scots would be clealry delineated as a separate language. For what it's worth, Scots is classified as a "regional or minority language" by the European Charter for Regional or Minority Languages, alongside Welsh, Cornish, Irish, Manx, and Scots Gaelic.
Scots developed out of a late form of Northumbrian Old English, and can be best understood as a separate development of Middle English. By the 18th century increasing literacy and scientific advancement led to a cultural cringe where many cultured people shunned Scots and wrote in English. From this point on, Scots (i.e. what we could call very broad 'vulgar' Scots) began to assimilate many Anglicisms- most strongly post WW2- leading to a language continuum, with English spoken with a Scottish accent at one end and Broad Scots at the other. Many Scottish slang terms are in fact remnants of Scots.
Scots or Scottish English should not be confused with Scots Gaelic, a Celtic language closely related to Irish and much more distantly to English.
Needs some WikiMagic.
Spoken in the Northeast of Scotland. The name for this variety arose as a comparison from the 'Attic' Scots spoken in Edinburgh, paralleling the rustic laconic speech of the Dorians in Greek history compared to the Athenians. (This has been used for TranslationConvention in translations of Ancient Greek plays, with Spartan characters being played with broad Doric and Athenians speaking in a more "refined" accent, be it Edinburgh or RP.)
Very harsh and hurried the futher North and East you go the more broad it becomes, The Other Wiki has lots of examples at http://en.wikipedia.org/wiki/Mid_Northern_Scots
Ya kin find a gid way ta spik Dorik at http://www.aboutaberdeen.com/doric.php as weil bit mind ya dinna ga a gleeg trying t'keep up.
The variety of Scots spoken in the Lowlands. ADrunkManLooksAtTheThistle is an example of a work written in Lallans with some other dialects thrown in, as is But'n'BenA-GoGo.
Also known as "The Banter". Spoken throughout Glasgow and the surrounding satellite towns. A localised and unique variety of Scots, influenced by 19th century Irish and F.L. Gaelic immigrants, and recently by Cockney through television. Like Cockney, it has its own unique rhyming slang.