I would like to understand the specific differences in power adapters that have similar input/output spec's but have different described purposes. In other words, can I use any power supply/adapter as long as the spec's are the same?

In this case, I have a hard disk system that has a supplied adapter that I suspect is bad. I have measured the voltage and it is within spec at 12.6Vdc. I do not know how to measure the amperage output without taking it apart, but I assume it is not outputting the needed amps because the hard disk enclosure does not start. So I want to first replace the power supply.
Power supply is:
Input: 100-240Vac
Output: 12Vdc up to 6.67A

If I order one from the manufacturer, it is $70. But there are many LED and general system power adapters on Amazon that have specs like:
Input: 100-240Vac
Output: 12Vdc up to 8A

for about $20. So what am I purchasing for $70 versus $20? I understand the mfr would be more for their own costs, but they're OEMing the product as well.

So am I safe in getting a 12Vdc 8A output power adapter, like LED purposed or other, or is there some specific reasons I *cannot* do this?