No one can tell you what construction means without some context. It's a very common word in syntax and generally refers to sentence constituents that may be more than one word. That's not very helpful.
However, inchoative (pronounced in KOE a tiv) has a very specific meaning -- Change of State. Which means beginnings, endings, and changes of all sorts; a pretty large semantic space, edging onto just about everything.
Inchoative and Causative are terms that are often used together; causative verbs like kill mean to cause some change to happen, and the change is an inchoative like die, which means 'become dead', while causative kill means 'cause to become dead'. Dead, die, kill are one triplet like that; white, whiten, whiten is another -- verb often the transitive causative has the same form as the intransitive inchoative.
Any verb that refers to a change of state is inchoative; frequently they're metaphors of motion verbs, like come and go. We use come to be and its contraction become as generalized inchoative markers -- He was tired ~ He became tired. In turn, come and go have their own causative relation with bring and take, respectively. Bring means 'cause to come' (Fred brought Alice/whisky/brownies/a gun to the party), and take means 'cause to go'.
The best example of inchoation (in ko A shun) in English is the verb get, which is the causative and the inchoative form of be:
- He is tired (stative) ~ He got tired (inchoative) ~ They got him tired (causative)
as well as the causative and the inchoative form of have:
- He has a new car ~ He got a new car ~ They got him a new car.
Since be and have constitute almost all the non-modal auxiliary verbs in English, that makes get very useful in all kinds of idioms that use those auxiliaries. This is where the famous equation of have got and have comes from, as well as the American use of gotten as an alternate past participle of get.
When I was learning Spanish in Mexico back in 1979-80, I was devastated to discover that, while it is otherwise an exemplary inflected language and a pleasure to speak, Spanish has no general inchoative verb, idiom, or other construction the likes of English get, which you can always mine for some way to indicate change of state.