Single joint...nutcracker/squeezing action...pressure on lips, bars and tongue. Not great if you have a horse with a small mouth or a low palate or a big tongue ie less room
French link...more even pressure on tongue, lips and bar..no squeezing. Bit more for the horse to play with.
Happy Mouth...I think this is just a comfort thing...nicer than a cold metal bit and more to play with?
as honeypots said really
some horse prefer jointed some french link
I had a happy mouth and it was a plastic one and the edges became sharp when horse played with bit so just be careful if using one