[somewhereoutth]

One way to see the difference is to consider a loop on the sphere or torus. On a sphere, any loop can always be drawn tighter until it is a point. On a torus, there will be some loops that cannot be drawn tight, as they go 'through the hole'. Another way is to imagine the sphere and the torus are hairy. You can comb a torus such that all hairs lie in more or less the same direction as their neighbours - if you try this with a sphere, there will be at least one point where the hairs completely diverge.