Heading Hold makes the aircraft stay on the heading it was at when you pressed the button, whereas Heading Select makes the aircraft fly at the heading selected on the Heading/Track window.
For example. If I use Heading Select, and 340 is displayed in the Heading/Track window, it will track 340^o. If I rotate the button to from 340 to 90, the aircraft will turn and track 90^o etc. Now if I press Heading Hold at 340, it will hold at 340^o, but if I want to head on track 90, I need to turn Heading Hold off, turn the aircraft to the heading of 90, then press the Heading Hold button again when heading at 90 to track 90^o.

In the image attached to my previous reply, once I see the Tooltip for Heading Select, I need to press the Right Mouse Button to activate it. As I said, it can take a few times to get it because a slight movement ove the mouse, and the Tooltip showing is lost, and clicking on the RMB does nothing.

This is the instructions for using Heading Select and Heading Hold from the manual for the 777 Captain for FSX/SE/P3D3:
Heading / Track (HDG/TRK) Reference Switch

Push - Alternately changes the heading / track window, PFD, and ND selected heading / track references between heading and track. Also changes the PFD roll flight mode annunciator, if the HDG or TRK mode is
engaged.

Heading / Track Window (Heading bug (select))
Displays the selected heading or track.
The selected heading or track is displayed on the PFD and ND.
If approach (APP) or localizer (LOC) is armed, the heading / track in the MCP window automatically changes to
the selected front course heading at LOC capture.
Displays 360 degrees when power is first applied.

And here is the instructions for Heading Hold;

Heading / Track Hold (HOLD) Switch (Autopilot heading hold on/off)
Push -
Selects heading hold (HDG HOLD) or track hold (TRK HOLD) as the roll mode
Displays HDG HOLD or TRK HOLD on the PFD roll flight mode annunciator
The AFDS commands wings level and holds the heading or track established when wings level is established.