The term "shift kit" is a registered trademark of TCI. But most kits designed to "hop up" an automatic transmission end up raising the line pressure so that it shifts up more firmly. The degree of firmness (or the less clutch slippage internally) depends on the type of kit, the degree of modification and the amount of throttle applied (in a TH350.)
When a kit is installed and the clutch slippage is decreased, the amount of heat build-up in the transmission can actually be decreased. Many people who install them claim that they help extend the life of a transmission by minimizing slippage, wear on the clutch surfaces and keeping the tranny cooler than it would normally run.
I like the way my El Camino [censored] with a B&M TransPak (Stage II) installed. There are 3 ways to install it and I took the middle option. It's the "street/strip" level of modification. Stage III is race only. It will chirp the tires on the 1-2 shift at anything over 1/2 throttle. Again, I like it that way.
If you want firm, crisp shifts, then a kit is the way to go. If you like smooth, gentle transitions from one gear to the next (even at full throttle) then the stock setup is probably the best choice.
As far as "stall", they're referring to stall speed of the torque converter. That's the maximum speed the TC will allow the engine to rev to without turning the transmission input shaft. (That's the nutshell version.) If you powerbrake an automatic transmissioned car or truck, the stall speed is where the tach stops climbing and stays steady...without beginning to turn the rear wheels.
Most stock converters are in the 1200-1800 rpm range. But many hopped up motors don't develop much power at that speed. So a looser converter allows the motor to spool up to a higher rpm before it stalls. If you have a motor that "gets on the cam" at around 3000 rpm, then a 3000 or 3200 rpm converter would work well for maximizing performance.
Cheap high-stall converters will almost always require the motor to come up to the stall speed before starting to move the vehicle. But decent ones (B&M, TCI, Midwest, etc.) will behave very much like a stock converter at light throttle application, but will flash up to the higher stall speed when more (or full) power is applied.
I have a 2400 rpm converter in my El Camino with a mild 400 smallblock. It's a little too low to be absolutely correct, because the motor really wakes up at about 2800 rpm. But it's a lot better than the stock converter was. And adding 3.73 gears helped, too (it had 2.73s in it stock and it was a dog off the line.)
hth,