Romans 5:14 "type"?

So this verse really was hard for me to understand because it said "Adam, who is a type of Him who was to come." So the Him give it away that it is comparing Adam to Jesus but I was thinking "why would Paul say Adam was similar to Jesus or that Jesus was the next generation of Adam." I didn't get it until I went to my old trusty friend "webster". He says type is:

1 a: a person or thing (as in the Old Testament) believed to foreshadow another (as in the New Testament) b: one having qualities of a higher category : model c: a lower taxonomic category selected as a standard of reference for a higher category ; also : a specimen or series of specimens on which a taxonomic species or subspecies is actually based

It blew my mind that it was talking about the Bible in the first definition, pretty cool. Then it clarifies to me that Paul is not saying Adam & Christ are alike. Paul is saying that Christ is the "higher category". Now I understand why some versions say Adam was the "first man" and Christ was the "second man" in 1 Corinthians 15:45. Adam was the first generation. Through his succombing to temptation he set a presidence for all mankind to succomb to temptations. Christ is the second generation and also the last. Through his abstenance from temptation, he set a presidence for all mankind to elevate themselves through Him above all temptations.