Yes, Atmega328P-PU is the actual microcontroller. They are available as 10MHz and 20MHz parts.
Note that this one does not have a bootloader installed.
You can use the Arduino you buy to install one.
Or you can buy one with the bootloader installed.
The DIP package can be easily replaced, the quad flat pack not so much. Quad flat package just describes the part package.
"Professionals" use both. Depends on the project need. I use both. I use the ATmega2560 also, you can find that microcontroller on the Mega board.
Board examples I've made are here Cross Roads Electronics