Is a turbocharged piston aircraft the same thing as turboprop?
They are both internal combustion engines that have a turbine in their exhaust that is used to power a compressor to pressurize the air before it is used for combustion.

In the turboprop, the turbine also powers the prop.  In between the compressor and turbine, the fuel/air mixture is burnt without significant moving parts.  Without the turbine and compressor, a turbine engine is essentially a tube with heating element in it.

In a turbocharged piston engine, you have an otherwise normal piston engine which turns the prop.  The turbine is in the exhaust from the piston engine and powers the compressor pushing air into the piston engine.  The turbine and compressor are not connected to the prop though.

Here they are as diagrams along with some other types of engine.