No, although some principles are common to both design methodologies.
Passive Solar Design largely relies on an optimised solar design and cross-ventilation from openings around the building to create a comfortable indoor environment. Thermal mass is also used to regulate and even out temperature swings by absorbing heat during hot periods and releasing the stored energy during cold periods. Occupants typically need to actively operate the building to regulate temperatures and air flows, shading thermal mass in summer and strategically opening windows to suit prevailing breezes.
The Passivhaus standard is far more flexible.
While the Passivhaus standard encourages optimised solar design, it isn’t reliant on it and a Passivhaus building can be better suited to sites where solar access isn’t optimal or where views lines aren’t orientated favourably but the outlook still should be captured.
The Passivhaus standard is better suited to locations where noise, pollution, security, or climate extremes are considerations, as indoor air quality isn’t reliant on occupants regularly opening windows and doors – regardless of the outside conditions – to bring fresh air into the building.
Thermal mass isn’t necessary for Passivhaus design either, with light weight construction suitable for some regions and climates.
Airtightness, air quality, condensation risk and mould growth risk aren’t typically analysed when adopting the Passive Solar Design methodology, whereas the Passivhaus standard requires these matters to be rigorously analysed, quantified, and tested to ensure an optimal outcome.