Those are two different systems which work differently and are run by separate DHS agencies.

Global Entry is run by the CBP and is used to clear immigration/passport controls when entering the US from abroad. Your passport is linked to the PASSID, your Known Traveler Number (KTN), which is identified by the facial recognition kiosks (most likely after the CBP gets the advance passenger information manifest, which has passport information, from the airline).

The PreCheck program at airport security checkpoints is run by the TSA. In order for you to qualify to use the PreCheck lanes, your KTN must be included in your reservation or Passenger Name Record (with a participating airline, most do); you should add it to your frequent flyer programs profiles. The PreCheck designation will then appear on your boarding passes.