Is this a faulty GFCI receptacle?
The GFCI device only protects part of the circuit, that's why there's a difference between the breaker tripping and the GFCI device tripping. When the GFCI is tripped, only the protected items lose power. When the breaker trips, the entire circuit; including the GFCI and protected devices, loses power.

It sounds like you may have a serious problem, that you might want to have a professional investigate.