Celica Hobby - [INTERIOR] Shifters, Stock vs Sport (SS)

What's the difference between my stock shifter and a short throw shifter (aka Short Shifter or "SS")?

The main difference in modified shifters is that the rubber mounts that insulate the stick from the lower shift mechanism and transmission have been removed. With these rubber mounts removed your car will shift more positively.

The rubber mounts in the stock shifter are there to lessen the vibration to your hands, if you race, I guess a little more vibration is acceptable.

A short throw shifter is simply a shorter stick. With a shorter stick you don't have to move your hand that far to shift, hence speeding up the shift process.

Keep in mind that with a shorter stick you may have to lean forward or adjust your seat position to reach the shifter comfortably.

When buying a new short shifter, you MAY want to look at getting a new boot for your stick or atleast modify the legnth of the boot before re-installing everything.

[added]
Is it normal for my shifter to vibrate or shake while driving ?

It's perfectly normal for your shifter to vibrate or shake while driving under throttle but not to make a rattling sound or noise. If your shifter makes a rattling noise it could be a loose shifter boot or other problem. Call your dealer for more details.