What is the difference between multiple allelism and polymorphism?
The term polymorphism is broad and can have different meanings. Here are your definitions

Multiple Allelism: The existence of more than two alleles of the same gene within a population.
Polymorphism: the occurrence of more than two distinct phenotypes of a trait in a population.

Considering your definitions only, then multiple allelism has to do with genetics while polymorphism has to do with the phenotype.
Most loci (=position in the genome) that contain more than one allele (=genetic variant) have no effect on the phenotype. So multiple allelism does not necessarily yield to phenotypic polymorphism.
On the other hand, plenty of phenotypic variation in a population is due to environmental variation (including what an individual eats) and not to genetic variation. So phenotypic polymorphism is not necessarily caused by a case of multiple allelism.