Cable qualifiers perform tests for opens, shorts, and whether a cable can support 10, 100, 1000 ethernet speeds. It does basic cabling tests and for a lot of installations it will suffice. Here's some info from a cable qualifier.

https://www.flukenetworks.com/datacom-cabling/copper-testing/CableIQ-Residential-Qualifier

A cable certifier does the same tests as cable qualifiers and more in depth testing and makes sure the cable plant meets TIA/EIA standards. It does checks for Insertion Loss, Crosstalk, and attenuation among many others. It also has features to fully document all tests performed and to provide printed results. Here's some info from one of the better certifiers in my opinion.

https://www.flukenetworks.com/datacom-cabling/copper-testing/dtx-cableanalyzer-series

A lot of times you'll read a cabling spec and the spec will specifically call for all cables to be certified and that printed results must be supplied. Ive even seen specs mention the DTX-1800 as one of the acceptable testing tools. In those type of situations a cable qualifier will never suffice.