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How does the root user locate executables?

A little while ago I was helping someone with running Python in a virtual environment, as root, for some specific purpose. I determined easily enough that this requires explicitly specifying the path to the virtual environment's Python executable (which to some extent defeats the purpose of the "virtual environment"); what I'm trying to understand is *why*.

When I activate a Python virtual environment (which modifies the PATH) and then try e.g. `sudo which python` I get a different result from `which python` (i.e. the Python that came with the OS install, rather than the one in the virtual environment); but `sudo echo $PATH` gives the same result as `echo $PATH` (i.e. the path to the virtual environment's `bin` subdirectory is present, and precedes the system Python path). If I actually run Python, I can similarly verify from within Python that different installations are found this way.

I had understood that locating an executable involves looking in each directory in the `PATH` environment variable, in order. I wouldn't be surprised if, say, `sudo` had to open a new shell, re-initialize everything and thus fail to see the change to `PATH`; but it clearly *does* see that change.

On my system, `which` is explicitly documented to "... [do] this by searching the PATH for executable files matching the names of the  arguments". That doesn't match the behaviour I see as root.

How is the root user locating the executable, and why is it different?