How do these two tripod types differ?
Aluminum tripods are made from an aluminum alloy that gives them a relatively good strength to weight ratio. Aluminum may not be as strong as carbon fibre but its weight and flexibility make it less prone to breakage. Rather than breaking, aluminum tends toward bending or denting when damaged by impact. This allows the tripod to still be usable in many cases. And, of course the price can be a bit lower when comparing apples to apples.
Carbon fibre tripods on the other hand have a very high strength to weight ratio. They are quite a bit lighter but able to support just as much weight as aluminum. Carbon fibre is manufactured by interspersing layers of the carbon fibre compound with layers of resin. There are different 'grades' of carbon fibre that can result in a varying tripod price range but in the long run they tend to be more expensive than aluminum.
Only the legs are actually made of carbon fibre. All the other components are either metal alloy or some kind or plastic. Being more rigid, carbon fibre can be prone to cracking if impacted.
Higher grade carbon fibre
Lower grade carbon fibre