Can anyone list the gaits of a horse in english and western riding? Ex: Walk, trot, canter, gallop, jog etc...
I think I know them all but I want to make sure.

Hoirses don't jog and the gaits are the same - English OR Western style:

"WALK:
The walk is a four-beat lateral gait. Each beat is distinct and can be easily heard. The walk is natural, and it is the slowest of the gaits.

TROT:
The trot is a two-beat diagonal gait. The right hind and left front move together, and the left hind and right front move together.

CANTER/LOPE:
Lope is another term for this gait, but it usually refers to the slow, western-pleasure style of cantering. While cantering, the horse is either on the left or right lead. The horse's left front leg is hitting the ground in front of the right, so the horse is on the left lead. A horse on the right lead would have its right leg hitting the ground in front of, not before, the left leg. When turning in a circle to the right, the horse should be on the right lead, and when turning to the left, should be on the left lead. So the horse should always be leading with it's inside leg.
A flying lead change is when the horse is cantered in a figure 8, and changes leads in mid stride when it reaches the middle of the 8, where it changes directions.
Most horses will canter on the correct lead naturally, and a few need to be trained to. A horse that is leading with its outside leg is said to be on the 'wrong lead', or moving with a 'false lead'. In some high-level competitions, horses may be required to do a "counter canter", that is, cantering on the wrong lead.

GALLOP - Or run. When the horse is fully extending itself in a run, there is a moment when all four feet are off the ground. It is usually a 4-beat gait, varying in speeds. Gallop speed is about 30 miles per hour. Here is the sequence of the gallop: 1. left hind; 2. right hind; 3. left fore; 4. right fore, followed by a moment when all four hooves are in the air."

http://www.ultimatehorsesite.com/info/gaits.html

Horse gaits are predicted on the horse only, not western or english. Here is website that explains this for you quite easily

Horses and horse training, care, tack, and supply info. › Horse Riding. Enter 'horse gaits' in the search section.

The exception is, of course, the Tennessee Walker that has gait ll its own. I could go into this in detail, but basically the website will refresh your memory.

It's how the rider sits and what signals he gives to the horse that causes the horse to change gaits.

ENGLISH
Walk, trot, canter, gallop
WESTERN
Walk, jog, lope, run