So far I understand that the saturated vapor pressure is the pressure exerted by a substance in liquid (or solid) vapor equilibrium, and that this pressure depends on the temperature of the system. Does the external pressure also affect the saturated vapor pressure of the system?
If we are treating the vapor like an ideal gas, the external pressure should be equal to the internal pressure. Else the gas will be expanding/contracting, and Pressure Volume and Temperature will be in flux. If Volume is a constant, then internal pressure changes with temperature. It may also help to think of temperature as a consequence of pressure and volume, like it emerges out of a system whose parts have an average kinetic energy.
The vapor pressure of a substance is a physical property of that substance which depends on the temperature of that substance, but does NOT depend on external pressure. Vapor pressure may be calculated with the Antoine equation, as seen here: https://en.wikipedia.org/wiki/Antoine_equation