Branches of linguistics. Synchronic vs diachronic approaches to the language study. Lexicology – ‘the science of the word’

Phraseological combinations (collocations) are:
clearly motivated;
made up of words possessing specific lexical valency which accounts for a certain degree of stability in such word-groups; variability of member-words is strictly limited.
e.g. to meet the demand, to make a mistake, to bear a grudge, to pay a compliment, to give a speech etc.
Phraseological unities are:
partially non-motivated, i.e. their meaning can usually be perceived through the metaphoric meaning of the whole unit.
e.g. to lose one’s head, a fish out of water, to show one’s teeth, to wash one’s dirty linen in public, to sit on the fence etc.
Phraseological fusions are:
completely non-motivated, i.e. the meaning of the components has no connection, at least synchronically, with the meaning of the whole group;
characerised by complete stability of the lexical components and the grammatical structure of the whole unit.
e.g. once in a blue moon, to be on the carpet, under the rose etc.
The Contextual Classification
Prof. Natalia N. Amosova Основы английской фразеологии (1963)
the contextual approach proceeds from the assumption that individual meanings of polysemantic words can be observed in certain contexts and may be viewed as dependent on these contexts;
a phraseological unit is a unit of fixed context characterised by specific and unchanging sequence of definite lexical components and a peculiar semantic relationship between them;
the two criteria of PhU – specialised meaning of the components and non-variability of context – display unilateral dependence.
According to whether or not one of the components of the whole word-group possesses specialised meaning, PhU are subdivided into:
phrasemes – two-member word-groups in which one of the members has specialised meaning dependent on the second component; the word served as a clue to the specialised meaning of one of the components is habitually used in its central meaning, e.g. small hours, black frost, white lie;
idioms – are semantically and grammatically inseparable units characterised by impossibilty of attaching meaning to the members of the group taken in isolation (as in red tape, dark horse), logical incompatibilty (as in mare’s nest).