The laptop wont have an issue.
The desktop will need an SSD tray (2.5 to 3.5" adapter) plus power and data cables if the original HDD isnt going to be removed.
Sata cables are not differentiated. A sata cable will work on sata1 drives or sata3 drives just fine.
I cant see pics but the sata power is the black end of this:
(the white end is a molex and extremely common in a pc)