Phase distance relay can see any fault. It acts on positive and negative sequence components so it can pick up on a slg fault. It should be a lot less sensitive than the ground distance relay for normal k values for ground faults.
a = 1 <120 deg
VA = V0 + V1 + V2
IA = I0 + I1 + I2
VC = V0 + a*V1 +a^2*V2
IC = I0 + a*IC + a^2*I2
VAC = VA - VC = V1-a*V1 + V2 - a^2*V2 >>>>> Line to line quantities have no zero sequence dependency
IAC = IA - IC = I1 - a*I1 + I2 - a^2*I2
ZAC = VAC/IAC
Ground distance relays can see all faults but its sensitivity to ground faults is dependent on the k value.
VA = (V0 + V1 + V2), IA = (I0 + I1 + I2)
ZA = VA/(IA + 3*k*I0) = (V0 + V1 + V2) / (I0 + I1 + I2 +3*k*I0) = (V0 + V1 + V2)/ (I1 + I2 + (3*K+1)*I0)
I think though ground distance relay will get the directionality wrong if it has negative sequence directionality and picks up for a phase to phase fault and vice versa. One of the GE relays I think the L90 has a note about DLG fault potentially causing the relay to the get the directionality wrong but I could never figure out from the manual why for sure that was.