Indeterminate or cordon are the ones that have a single stem that will keep on grpowing upwards for ever (hence indeterminate) and is grown on a cordon, that is tied to a cane. Side shoots are removed for best results. The fruit trusses grow from the main stem between every other leaf joint or so (and will grow similarly along side shoots if left to grow). Fruiting continues for the life of the plant burt in the UK 5 trusses is about the most you'll get in a season.
Determinate, don't go on for ever, they for a bush. The trusses form a the end of each side shoot. So you shouldn't take out the side shoots but they may well need to be supported by a cane. The fruiting tends to happen all at once.
In general, bush tomatoes are grown outdoors, cordon can be grown indoor or out (dependant on the variety).
There are also semi-determinate but they are normally grown as cordons.