A contraction is sometimes defined as an
abbreviation that includes the last letter, and in this case the word 'abbreviation' is used to mean one that does not.
Where the word is pronounced as its shortened form, an apostrophe is normally used: I've you're this'll and the poetic o'er e'er. But in poetic tho' thro' the apostrophe is interpreted as indicating omitted letters: you never see these as tho. thro.. The possessive S however is not a contraction of anything.1
Where the short form is not pronounced as such, but is only a written device for the full word, usage varies. Formerly a full stop was used, as in Dr. Mr. Rd., and this is still used in written American English. From about 1900, under the influence of the Oxford English Dictionary and Fowler, British usage changed to omit the full stop in contractions but not abbreviations, so Dr Mr Rd but still Prof. Str. ref. -- this usage is followed in all books by major publishers in Britain and countries that adhere to it rather than America in style, but in less formal writing the two styles both occur.
The contraction no. or No. for numero (number) is usually an exception because it would look too ambiguous if it wasn't clearly marked.2
The newer British style is also the French style, which uses M. for Monsieur but Mme Mlle for Madame and Mademoiselle.
Formerly the apostrophe was used at the beginning of clipped words, like 'bus 'phone. This habit is probably dead by now.
In old poetic forms like smil'd it indicated that the vowel e was omitted in speech, to fit the metre. Over the course of Middle English the loss of e in this position became usual, and its preservation in poetry rare, so eventually words written like smiled were treated as monosyllables and the extra vowel had to be special marked as e.g. smilèd if the poet wanted it to be sounded for the metre.
1. It was sometimes treated as if it was a contraction of 'his', and the expression Johnes house was written John his house, these being pronounced basically alike in Middle English; but this doesn't work for feminine possessives: Dianas house can't come from her. But the apostrophe might have been introduced in this belief.
2. And this often also preserves a once more widespread habit of raising the final letter: No yr usually also with a stop underneath.