Is it true to say that both a "shared server environment " and a "VPS environment" can be either IaaS or PaaS?
Usually, Only a VPS hosting can be either.

While an IaaS is always VPS, what's commonly called "shared hosting plan" is PaaS in which a client shares the same hardware and webserver software with different customers (due to sharing a webserver, it's not a VPS --- Virtual Private Server).

In a PaaS (of the subtype Pass;VPS) only the hardware is shared (so it's indeed a "shared server", but only in that sense).