What is the difference between multiple alleles and polygenic inheritance?
The difference is the number of strands of DNA involved.
In multiple alleles the same strand of DNA is involved. For example the blood type is found on the same strand of DNA. That strand can be occupied by a code that builds A type proteins, B type proteins or no proteins (Type O blood).
The polygenic inheritance is found on multiple strands of DNA. For example the formation of antibiotics to fight bacteria and other foreign bodies are found on multiple places on the DNA. These pieces of the proteins formed in multiple places can be combined in almost infinite combinations. This makes it possible for the immune system to respond to threats that may not have existed in a previous genetic generation.
In a similar manner enzyme proteins can be made from non continuous parts of the DNA. Being polygenic organisms can product enzymes to meet new challenges. A surprising example is the development of enzymes in some bacteria that can digest plastics. Polygenic inheritance makes for almost infinite possibilities