Well, you' re asking one whale of a question! I' ll try to give you a beginning primer.
' Spine' , as we archers use the word, means how much a given arrow will flex under a 2 pound weight placed in the center of the shaft. Over the years, they' ve figured out that an arrow that deflects .XXX of an inch will shoot well out of a bow that draws ZZ pounds. The less it deflects, the higher draw weight it will handle.
I' d like to get off the main point here and sidetrack a bit.
We really use the word ' spine' loosely and incorrectly. If you check an arrow at different points around it' s diameter, you' ll find one spot where it checks stiffer than at any other point around the shaft. That is the arrow' s actual spine, using the strict technical definition of the term. Actually, when everyone used wood arrows, we did use the word correctly because we always tested an arrow' s deflection across the stiffest portion of the arrow, which really was the arrow' s spine.
Anyway... back to the business at hand.
When you go from, say, a 100 grain tip to a 150 grain tip, you' ll need a stiffer arrow to carry it. And vice versa. If you shoot a 33" arrow at 50 pounds, you' ll need a stiffer arrow than someone else that shoots a 28" arrow at 50 pounds. You can adjust spine by using different points and cutting arrows to different lengths. An arrow that reacts weak in spine when you shoot it with a 125 grain point might shoot great with a 100 grain. Or, if you have enough arrow, you can try cutting off an inch and see how much it stiffens up. IF it acts too stiff, then you can try a heavier tip.
Things can get pretty complicated if you let it, but as long as you understand those few basic things about spine, then you' ll do just fine.
As far as the sizes on aluminum arrows, the sizes have absolutely nothing to do with spine. The first two numbers are the arrow' s diameter in 1/64ths of an inch. The second two numbers are the arrow' s wall thickness in 1/1000ths of an inch. So, a 2216 is 22/64ths inch in diameter with a .016" wall thickness. Generally speaking, the diameter of the arrow relates more to spine and the wall thickness, even though it does have an affect on spine, it relates more to durability and weight.
But there are many different aluminums with different diameters and different wall thicknesses that overlap in spine. Say your bow shoots 2018' s well, but you want a bit faster arrow. You look at the charts and see that the 2213 is in the same spine range as your 2018' s, but weighs some 80 grains less. The tradeoff you make for a little faster arrow is in durability, because the 2213 is thinner walled than the 2018.
Carbons are a different beast altogether, as I guess you' ve already found out. Some mark their sizes by the spine range they cover, like GoldTips and those Carbon Express Terminators I like. Some, like Beman, size their arrows by their deflection. Others just seem to pull a number out of thin air and slap it on.
Hope that clears up some of your confusion.