Exact

There are two different words - homonyms - written exact. (There is an obsolete third.)

• The (current) adjective exact (OED's exact, adj.¹) is the most common of these. It now means 'precise','accurate'; 'rigorous in detail'. (It used also to mean 'refined', 'well designed', 'highly skilled'; 'elaborate'.)
• The verb 'to exact' has the broad meaning of "[t]o demand and enforce the payment of (fees, money, taxes, tolls, penalties, etc.)" (OED, 1894 s.v. exact, v.). This meaning is largely to do with money, but the verb can be extended to include other obligations, such as labour or duty.
  • This gives rise to the participial adjective exacting - 'demanding', 'difficult'; of a task, or of the person who imposes the task; "[t]hat requires or is disposed to require too great advantages, exertions, or sacrifices" (OED, 1894, s.v. exacting).
  • An exaction is something demanded, like a tax payment (particularly one of which the speaker disapproves or resents). The preferred form of the abstract noun is exactitude (rather than 'exactness'). A related adjective is exigent.
    • • OED's exact, adj.² is a 'rare' and obsolete adjective, of which the only meaning given is "Drawn forth by descent, descended".

Etymological note: it may surprise the reader, as it surprised the current writer, to learn that all these words share a root, the Latin verb exigĕre, which has many strands of meaning. The past participle is exactus (exacta in the feminine singular). The adjective (¹) is derived from the senses (1) 'highly finished, consummate' (from the verb in the sense 'to complete', 'bring to perfection'); and (2) 'accurate, precise', from the verb in the sense 'to calculate precisely'. The verb is also derived from exactus, formed from exigĕre (from ex, here 'out') and agĕre ('to drive'). The literal sense is thus 'to drive or force out'; hence the various derivative senses 'to demand, require'; 'to try, weigh accurately'; 'to complete, bring to perfection'.