I am wiring a relay into a pump and right now they are using twist type connectors. Can I use end terminal connectors instead of twist type connectors? In which situation are end terminal connectors properly used.
There are all kinds of terminals but if you use the quick-disconnect type that will be better than a wire nut if you're disconnecting and reconnecting at times.
If the wires are inside an enclosure, you could also use a terminate the wire with ring or spade terminals and a terminal block / terminal strip the right size, which is sometimes nice because you can put a meter on the screws in the terminal strip when testing.
You can use any connector that is listed for the use, and rated to accept the number and size of conductors being connected.
If you check with the manufacturer of the connector, they should have a list of acceptable wire combinations that the connector can be used with.