How can you differentiate between a laptop hard drive and a desktop hard drive

Usually by the physical size of the device.

Typically desktop drives come in a 3.5″ enclosure like this;

(nowadays there are exceptions for SSD disks)

Laptop drives are usually 2.5″ or sometimes 1.8″ like this;

It is possible to use a laptop drive (both traditional mechanical, spinning disk and SSD) in a desktop, but not a desktop drive in a laptop. As you can see physical space for the desktop drive inside the laptop is usually the constraint.