Those are just straight-blade spade connectors.
Yes, just pull harder but pull at the connector or as close to it as possible to keep the wire from separating from the connector. Sometimes I'll use 1 pair of needle nose pliers and a flat-blade screwdriver to gently pry them off.
The item on the left is your overload. The item on the right is your start relay.
I've replaced several of these over the years. It seems they have some universal replacements that are classed by HP of the compressor. They are usually pretty cheap - $10-$20.
EDIT: I just saw that you didn't hear any clicking noises. Usually when the relay fails, the overload will keep opening the circuit (making a 'click') to prevent damage to the compressor when it fails to start quickly. I'm not sure then exactly what's going on.