Both. SPD's (the electronic kind, most common for 60 Hz these days) are simply Metal Oxide Varistors (MOV's). These are simply electronic devices that "cutover" from Open Circuit below a threshold voltage to Short Circuit above that threshold voltage in fractions of a microsecond. If you had a Perfect Super-conducting (zero Ohms) connection from the SPD to the Ground that could handle unlimited current (and if the SPD could handle unlimited power forever), then surge would be clamped to 0V for the time the voltage is above cutover. This is of course not the case in reality. The biggest limitation is the power handling capability of the SPD before it dies. The "ground" connection matters very little as the SPD is in parallel with the connected equipment, so if the SPD goes to "short circuit", the voltage across the connected equipment should be close to zero, regardless of the voltage from the ground bus to the actual Earth.
Mark