On the package (or on the Internet, if you look them up), vining types are called indeterminates, and bush types are called determinates.

To add to what queuetue said...

Watch out when pruning determinate (bush-type) plants because they only put out fruits on the ends of their growth. They'll still need to be pruned, very selectively, so that only the strongest leads survive but remember, since you're only going to get fruits on the very ends of those vines you're reducing your harvest with each cut. Still, some sacrifices need to be made to keep the plant from become unwieldy or too large for it's structure (cage, trellis, stakes)

Indeterminate (vining-type) plants put out flowers all along their vines and pruning back suckers and only keeping three or four leads of the main vine will help direct the plant into producing larger fruits throughout it's season... whereas if you didn't prune it much of it's energy would be wasted into creating dozens of off-shooting vines and you would only get one big harvest (of relatively small fruits) at the end of the season just before the first frost...and sometimes not quite just before the first frost and you lose everything.

Personally I prefer the indeterminate vining-types because they are easier to train along a trellis instead of using cages or stakes.

It also depends on the type of tomatoes you are after. For instance, if you are looking for a good beefsteak tomato, your going to be going indeterminate vine. On the other hand, if you are looking for plums/Roma for sauces, then determinate bushes are going to be your only real option.

For me personally, I have three vines growing in my SFG, and 4 bush Romas growing up on the deck in large clay pots. Judging by the size of the Romas in the pots, I would really think twice about putting them in the SFG, especially at 1/SF. I would think the minimum would be 2/3SF.

If you want to grow plums/romas, you do have options other than determinant. There are plenty of indeterminant varieties to choose from: Juliet, Golden Rave, Olivade, San Marzano, Debarao, and Geronimo for starters....

I put both in, 8 indeterminates (sadly 4 are in my compost pile now) in trenches and then 2 bush tomatoes for an early crop so I can try my hand at canning.

The bush tomatoes are going crazy, I planted them in a 4 square foot block, which is being filled out by the tomatoes. The good thing about the bush type too, is that you should be able to replant the square with a new crop for fall.