| Ratchet shifters move one gear position at a time. Push it forward or pull it back and it only moves one position. You need to ratchet it again to move into the next position. Starting all the way back in first gear, you push the shifter forward into second. When you release the shifter, the handle comes back into a neutral position waiting for the next shift. You push it ahead again and you're in third gear and the handle comes back for the next gear. So it's always push, release, push, release.
Gate shifters use a "gate" to move the shifter through the gears. The gate is normally designed so it will only move one gear at a time. Starting all the way back in first gear you would push the shifter up into second. The handle will stay in that position. From there, the shifter would move over before it could be moved up into third. That's the "gate".
Ratchet shifters are not common in a street car. You're ratcheting it back and forth through the gears and need to rely on an indicator to tell you what gear you're in because the handle is always in a center neutral position. A gate shifter can be moved through the gears quicker depending on the gate design and you can easily look at where the handle is to know what gear position you're in.
I like the ratchet shifter in my race car. The handle is always in the same position. When I shift, I slam the handle forward with no worry about going into the next gear. Actually that's not really true. I have a 2 speed tranny. I launch in first, slam into second around the 1/8 mile mark then push it forward into neutral after I cross the finish line. There's an interlock that needs to be pushed preventing me from pushing it into reverse be accident even though nothing would happen anyway. I have no reverse gear unless the transbrake button is pushed at the same time.
Which shifter is better depends on your own opinion. Both are popular. It depends what you like. I had a B&M megashifter for a while and didn't like it. I now run a B&M Pro Ratchet. I've considered going to a gate shifter which would allow me to use an air/electric shift device to do that 1-2 shift for me controlled by an rpm switch. | 
