I'll briefly say the ones off the top of my head:
1 def pure: 1 def obviously. Att, str, range, and mage range from anywhere to anywhere. (The most versatile pure)
20 def: "Void pure" "Initiate pure" Usually a 1 def pure who messes up and gets 3-5 def then decides to get 20. At 20 def you can wear Void, Initiate, Mystic, and Infinity armors.
Zerker: Back in the day zerkers usually had whips (70+ atack) & 45 def for berserker helmet. Now they all seem to have 60 attack and turmoil and KO with d claws.
Barrows pure: High attack, high strength, 70 defence. Barrows pures were originally invented to get huge hits in edgeville wild with Dharok's set. I feel like the value of barrows pures has declined as now they are forced to hybrid or use AGS.
Tank: Low att, low str, high defence. High range and high magic. The most common tank is a range tank with vengeance. The idea is to have high defence to make up for the weak armor (dragonhide) and high range obviously to hit high. At higher levels, it's very hard to KO with range unless you have vengeance.
Staker: There are many, many types of stakers. But typically they have 1 prayer and 1 summoning to keep their combat level low.
I hope this helps, these are the main types of pure. I only recently started playing again so I hope my knowledge isnt too old school >_<
