What is the main difference between alpha and beta radioactive decay?

Basically,

Alpha decay occurs when a nucleus (of an atom) gives off 2 protons and 2 neutrons.

In Beta Decay, a neutron converts into a proton, and then releases an electron.

(Remember that neutrons have no charge, which means they are consisted of protons (+) and electrons (-) to form a neutral charge.)

salters chem open-book by any chance??

I think the main difference is the type of radioactive particles which are emitted e.g. alpha particle/helium nuclei for alpha-decay and beta particle/electron for beta-decay. in alpha-decay the nucleus disintegrates, and in beta-decay the nucleus is converted...
Also alpha-decay is meant to occur in heavier elements.  

For the second bit: natural radioactive decay occurs naturally due to an unstable nucleus, but nuclear fission doesn't occur naturally. The nucleus of the element has to be hit by a neutron before fission can occur. on earth this is slow and spontaneous, so fission is usually artificially induced.

hope this helps