Do thin hard drives work on older laptop models?

This is my first time shopping for hard drives and i'm doing it because the original hard drive on my laptop died and my backup hard drive (taken from an old laptop) might fail as well (given that it's close to a decade old). I wanted to get a 250 to 500 gb hard drive with 7200 rpm but during my search i noticed that most hard drives for laptops are now very thin. But i can't find any information confirming if it'll work on the older models (my model is a lenovo ideapad z560) or if there'll be compatibility issues. I would really appreciate any and all information that can be given to me, thank you in advance!

ps: It would also be great if you could recommend a laptop hard drive brand or model!

Should be a go, there's no straight-forward info on whether it is SATA or ATAPI, but can't really believe 500 stock is anything else besides SATA, that z560 is like 3 years old, where the "decade" old come from?

Thinness has nothing to do with it besides desktop/laptop, just ascertain SATA/ATAPI and you are fine.

Both your answers are correct an incorrect.
Your broken drive in your lenovo ideapad z560 is a SATA drive. SATA being the type of interface.
Your old drive depending on how old is likely to be a PATA (IDE) so not compatible

The size of a laptop is usually referred to by Form Factor (how ever they arrive at that) and 2.5" drives are for laptops ie smaller,
12.5mm drives in height are usually for more recent in larger data drives That is because of the introduction of an extra platter.

So check your drive's interface type

As Andy said, you need to be sure whether it is SATA or PATA.
Laptop drives generally come in the speeds of 4200 and 5400 RPM.

Older laptops used 12.5mm drives if I recall correctly, modern one are 9mm. If you get a 9mm, you will want to put something in there to fill the space so the drive isn't flopping around.