Scottish English is usually taken to mean the standard form of the English language used in Scotland, often termed Scottish Standard English. It is the language normally used in formal, non-fiction written texts in Scotland. Although the terminology has often been used vaguely, modern usage distinguishes clearly between Scottish English and Scots.

Background
Scottish English has a number of lexical items which are rare in other forms of standard English. General items are outwith, meaning outside of; pinkie for little finger; and wee, the Scots word for small (which also occurs in Hiberno-English). Culturally specific items like caber, haggis, and landward for rural.
In some areas there is a substantial; examples include gadge (lad, chap) and peeve (alcoholic drink).
There is a wide range of (often anglicised) legal and administrative vocabulary inherited from Scots, e.g., depute /ˈdɛpjut/ for deputy, proven /ˈproːvən/ for proved, interdict for injunction and sheriff substitute for acting sheriff.
Often, lexical differences between Scottish English and Southern Standard English are simply differences in the distribution of shared lexis, such as stay for "live" (as in: where do you stay?); doubt for "think the worst" (I doubt it will rain meaning "I fear it will rain"). Correct is often preferred to right (meaning "morally right" or "just") when the speaker means "factually accurate".

Lexis
An example of a Scottish male with a middle-class Renfrewshire accent (help·info)
While pronunciation features vary among speakers (depending on region and social status), there are a number of phonological aspects characteristic of Scottish English:

Scottish English is a rhotic accent, meaning /r/ is pronounced in the syllable coda. As with Standard English (RP), /r/ may be an alveolar approximant ([ɹ], although it is also common that a speaker will use an alveolar tap [ɾ]. Less common is use of the alveolar trill [r] (hereafter, <r> will be used to denote any rhotic consonant).

• While other dialects have merged /ɛ/, /ɪ/, /ʌ/ before /r/, Scottish English makes a distinction between the vowels in herd, bird, and curd.
  Many varieties contrast /o/ and /ɔ/ before /r/ so that hoarse and horse are pronounced differently.
  /or/ and /ur/ are contrasted so that shore and sure are pronounced differently, as are pour and poor.
  There is a distinction between /w/ and /ʍ/ (also analyzed as /hw/ in word pairs such as witch and which
  The phoneme /x/ is common in names and in SSE's many Gaelic and Scots borrowings, so much so that it is often taught to incomers, particularly for "ch" in loch. Some Scottish speakers use it in words of Greek origin as well, such as technical, patriarch, etc. (Wells 1982, 408).
  /l/ is usually velarized (see dark l). In areas where Scottish Gaelic was spoken until recently (such as Dumfries and Galloway, velarization may be absent.
  Vowel length is generally regarded as non-phonemic, although a distinctive part of Scottish English is the Scots vowel length rule (Scobbie et al. 1999). Certain vowels (such as /i/, /u/, and /ae/ are generally long but are shortened before nasals and voiced plosives. However, this does not occur across morpheme boundaries so that crude contrasts with crewed, need with kneed and side with sighed.
  Scottish English has no /ʊ/, instead transferring Scots /u/. Phonetically, this vowel may be more front, being pronounced as [ʉ] or even [y]. Thus pull and pool are homophones.
  Cot and caught are not differentiated as in some other dialects.
  /θs/ is often used in plural nouns where southern English has /ðz/ (baths, youths, etc). with is pronounced with θ. (See Pronunciation of English th.)
  In colloquial speech (especially among young males), the glottal stop may be an allophone of /t/ after a vowel, as in /ˈbʌʔər/. These same speakers may "drop the g" in the suffix -ing and debuccalize /θ/ to [h] in certain contexts. Phonology
  Syntactical differences are few though the progressive verb forms are used rather more frequently than in other varieties of standard English, for example with some stative verbs (I'm wanting a drink). The future progressive frequently implies an assumption (You'll be coming from Glasgow).
  Prepositions are often used differently. Most Scots would say different from where in the south there is a strong preference for different to. The compound preposition off of is often used parallel to English into (Take that off of the table).
  
  Scots and Scottish English
  
  Abercrombie, D. (1979). "The accents of Standard English in Scotland.", in In A. J. Aitken & T. McArthur (eds.),: Languages of Scotland. Edinburgh: Chambers, 65–84. 
  Aitken, A. J. (1979) "Scottish speech: a historical view with special reference to the Standard English of Scotland" in A. J. Aitken and Tom McArthur eds. Languages of Scotland, Edinburgh: Chambers, 85-118. Updated in next.
  Corbett, John, J. Derrick McClure, and Jane Stuart-Smith (eds.) (2003). Edinburgh Student Companion to Scots. Edinburgh: Edinburgh University Press. ISBN 0-7486-1596-2. 
  Foulkes, Paul; & Docherty, Gerard. J. (Eds.) (1999). Urban Voices: Accent Studies in the British Isles. London: Arnold. ISBN 0-340-70608-2. 
  Macafee, C. (2004). "Scots and Scottish English.", in In Hikey R.(ed.),: Legacies of Colonial English: Studies in Transported Dialects. Cambridge: CUP. 
  Hughes, A., Trudgill, P. & Watt, D. (Eds.) (2005). English Accents and Dialects (4th Ed.). London: Arnold. ISBN 0-340-88718-4. 
  Scobbie, James M., Nigel Hewlett, and Alice Turk (1999). "Standard English in Edinburgh and Glasgow: The Scottish Vowel Length Rule revealed.", in In Paul Foulkes & Gerard J. Docherty (eds.),: Urban Voices: Accent Studies in the British Isles. London: Arnold, 230–245. 
  Wells, John C. (1982). Accents of English. Cambridge: Cambridge University Press. ISBN 0-521-22919-7 (vol. 1), ISBN 0-521-24224-X (vol. 2), ISBN 0-521-24225-8 (vol. 3).