Can anyone help me out! I'm not sure what they call those small sata HDD for laptops,what's the name of the HDD that is found within laptops. Do we call it small sata hard-drive or it has its own name?

And again does it affect the drive if you install the OS on that small sata drive using a computer ?
Thanks

Laptop drives are 2.5 inch as opposed to the larger 3.5 inch ones for desktops.
They don't have a special name, as such.

I can't answer your supplemental question as it doesn't make much sense.