In a atomic quantum system, typically discussing in quantum optics, there is something called dark state. A dark state is a state of a quantum system that does not emit any photon. A ground state also does not emit photon as well. Therefore, what is the different between a dark state and a ground state?
The emission or absorption of a photon depends on the state CHANGE of an electron (or other particle).
Hence a particle emits a photon when going from a state to another state at lower energy. It absorbs a photon when the transition is to a state with higher energy. The energy of the photon is equal to the difference in energy of the two states.
A dark state does not emit OR absorb a photon, usually because transitions from or to the dark state are forbidden (according with the quantum selection rules).
Hence a dark state cannot be observed (with conventional methods).
The ground state cannot emit a photon since it is the lowest energy state (so there is no transition allowed to lower energies), but it can clearly absorb a photon, so it can be "observed".
Note that we do NOT observe, EVER, "absolute energies" but always the energy change from one state to another (this is true also in classical mechanics). Usually the reference set as ZERO is the "vacuum level" (basically a free particle with no interaction).
This why the ground state of the Hydrogen electron is -13,6 eV, ie you need a photon with that energy to completely free the electron from the atom.
So we can observe the ground state of the hydrogen atom this way (and also with the transitions to other states).
Now if Hydrogen would have a state between vacuum and ground state where no transition from the ground state is allowed, that would be a dark state.