As far as I know there is not a specific designation for a semi auto AK-47, as compared to the M4/AR-15 categories, they all fall under the same moniker. Semi auto versions of specific AK type rifles even keep their select fire brothers model designations i.e. the AMD-65. Select fire or semi only still an AMD-65.
An assault rifle is a select-fire (either fully automatic or burst capable) rifle that uses an intermediate cartridge and a detachable magazine. It is not to be confused with assault weapons. Assault rifles are the standard service rifles in most modern armies. Assault rifles are categorized in between light machine guns, which are intended more for sustained automatic fire in a light support role, and submachine guns, which fire a pistol cartridge rather than a rifle cartridge.