They come in PATA and SATA style, you need to know which type of drive is in the laptop. The caddy that you linked to goes in a CD/DVD bay, and requires the computer be working (obviously, I hope). The external enclosure allows you to hook the hard drive to any computer that has a USB port. Short version, you won't lose any files just because you lose the motherboard.
I have 2 WD book drives that the case/port went bad and was wondering if there is a caddy that would work for them? I ripped one open but the oldest one I haven’t touched so far. They’re pretty old.