In relation to the new consoles.
The Ps5 is supposed to have fake ray tracing and the XboxSeriesX real one.
No, there's only one difference between software ray tracing and hardware ray tracing.
Both new consoles can do BOTH methods.
Software = The game itself programs the ray tracing via the graphics card, this is also possible on PS4 and XBox One, but it is rather "cheap" and at most useful with a few reflections.
Hardware = The game raytraces the (mostly) complete lighting via the raytracing unit of the graphics card. With this you can show "real" effects.