curb bit 
Bit composed of a mouth and two side bars; it lowers the horse’s nose.
sliding cheek bit
Bit whose mouth slides up and down the cheeks; this action is gentler to the horse but provides slightly less control.
Bit that can be used alone; it combines the characteristics of the snaffle and curb bits.
jointed mouth bit
Curb bit whose mouth is composed of two articulated parts; it is gentler to the horse than a straight mouth bit.