Actually. Both of the words came from same orgin. In Arabic, inşaat derived from the word "inşa". The root of the word "N-Ş-E". Its meaning is to be born. İnşa is the active form of n-ş-e. Its meaning is to make smth to be born. "İnşa" in its root means making something to be born. But in Turkish usage we use that word differently. For instance we say "Bu yapıyı ben inşa ettim" " I constructed or made this building or place". The antonym of inşa is "imha" which means demolish. The word inşaat used in Turkish naming finished or unfinished building blocks. For instance we say " Bu inşaatın sahibi babam" The owner of the building (inşaat) is my father". We can also say " Apartman inşaat halinde" The apartment is in the condition of "building".

İnşa is more used for the action of building. İnşaat is more used for what is built, buildings.

if you say inşa it means build if you say inşaat it means building something you build.

"İnşa"= Verb "İnşaat"= Noun

"inşa etmek" is a verb means to build "inşaat" is a noun means bulding that has not finished yet.