Oat groats are the whole grain.
Steel cut oats (aka Irish oatmeal as well as pinhead oats) are the whole grains chopped into little pieces.
Rolled oats are the grains put through heavy rollers so they become flat flakes.
Oatmeal can be made of actual oatmeal (rolled oats chopped up) or rolled oats (as in porridge).
I only give them sprouts during the spring, summer and a bit when they are molting. I don't give them any sprouts whatsoever during the resting season (winter) because I believe that making the diet richer in the warm months and poorer in the cold ones helps their bodies to mark the different seasons.
I use a soaking/sprouting mix for canaries I get at ABBA which is made of small seeds (
http://www.abbaseed.com/Seed_Products/SOAK/soak.html - but you can get it in the net from bird food places like foryourbird.com or allparrotproducts.com) and sprout it until I see green 'tails' (they grow white ones first but I wait until they have the green ones) then I mix them with the gloop. I only make enough for two days because you don't want it to go sour.