I think "turbo intake" is a general term people are using to differentiate as you have an intake manifold and a intake attached to the turbo. Turbo intake, cold air intake one in the same

Your turbo has no intake like no pipe, no filter or nothing at all?

So you can see your inducer wheel in the turbo? No plastic/rubber hose going from turbo inlet to MAF. Without a pipe and filter going up you can easily suck water or debris into the turbo then the motor and hydro-lock and all types of horrendous activitys?
Judging from your picture on your profile, you do have a stock Intake tube that is recirculated and stock MAF but looks like your air box was removed and a filter in place.

Yep you should have a filter at the least otherwise you sucking in dirt into the engine.