Paints and primers are all designed for varying types of surface conditions. Most homeowner paint and primer products are latex (water) based or alkyd (oil) based. Some are designed to be obsorbed, penitrating into a surface, providing good bonding power for the top coat, while others are designed to sit on top of a surface and bond chemically like higher proforming metal primers. There are many other high preformance epoxy primers for other more harsh coonditions.

Primers are often sealers too - usually when applied to new surfaces like drywall, plaster, wood, or CMU they provide a moisture barrier and once top coated, the surface is able to hold out moisture - which is a prime cause of coating failures. Once top coated, the properly prepared and primed surface will provide long lasting service for the homeowner.

Drying times to touch or recoat can vary greatly depending on the product being applied. When in doubt, ask you paint store professional which primer is best for your situation and needs.

The slow dry one does state "Assures excellent gloss and color of enamel topcoats". The quick dry states "Assures uniform appearance of topcoats".

It means that they both have good enamel holdout. No need to switch to a slower drying primer.

Michael