H3 High Pressure Switch Fault
This is stating that there is a fault with the High Pressure Switch. The fault occurs when the system is in an off state but is still registering that the high pressure switch is open circuit. This switch can be measured with a multimeter and should be closed circuit in a normal state and open for a high pressure state.

E3 High Pressure Switch Activation
This is stating that there has been a high pressure error on the system. This could be due to fan motor or air flow problems but could also be an issue with the high pressure sensor or switch.

In this case, the switch was going into an open circuit intermittently. Even when there was no high pressure issues. In this video I replace the High Pressure Switch.