The linear supply will likely have sinusoidal ripple at 1x or 2x the power line frequency. So, look at the supply witch your scope AC coupled while measuring DC.
The resistance of the input terminals is a good first clue.
Some are AC. some just unfiltered DC and some are regulated DC and some are SMPS.
I've found the most reliable test is the weight .. .. I've been through a box of wall warts collected over time and the linears are significantly heavier - transformer tonnage ..
Also, I'd find the linear bzzz difficult to distinguish from the 5ohz hum from my zimmer frame