It sounds to me like an Arduino Uno clone.
Why it says "For Arduino UNO R3"?
I would read that as "For Arduino UNO R3 projects" (ie. Uno-compatible).
Isn't it actually an "Arduino UNO R3
No, it's a clone. Or not really a clone (see below) because they used different hardware. It is compatible with the Uno in most respects.
What are MEGA328P?
That is the main chip on the board (actually an Atmega328P).
They have saved money by using a CH340 USB-to-serial chip instead of the Atmega16U2 used on genuine Uno boards. You may need to install a different driver to make that work. I disagree with the other answer(s) that this is a separate board or chip. It is clear from the photo of the chip near the USB socket that it is a CH340 chip there. See, for example https://hackaday.com/tag/ch340/ from which I quote:
The cheapest USB to serial chip on the market appears to be the CH340G, available for 20-40 cents apiece from the usual retailers. There is, however, almost no English documentation, and the datasheet for the CH340 family doesn’t include this chip
They used it because it is cheap.
Does "Arduino UNO R3" comes with other chipsets?
Yes the genuine one comes with an Atmega328P (main processor) and Atmega16U2 (USB interface).
Having said all that, the Uno is a good all-rounder starting board to get going with Arduinos.
Note that they are using the SMD (surface mounted) main processor chip. If you fry it you need to replace the whole board, not just the chip. However the entire board is quite cheap. :)