That confused you all? I would sincerely hope it did not confuse your electrician.

Your new oven draws 3600 watts at FULL load @ 120/240v. A watt is a watt. At that point amperage is determined by the voltage. At full load this is a nominal 15 amps. This is NOT a 15 amp circuit.

Why did you call Lowes about this? All they did was sell you the thing. They are most often clueless about these matters and often give anywhere from erroneous to downright dangerous advice.

Unless the instructions SPECIFICALLY state so, all you need is a 120/240v-20 amp circuit for this appliance. Since this unit requires 120 & 240 volts you must run a 4-wire cable in the XX/3 variety. Such as 12/3 (with ground) NM cable.
IF the unit required a 30 amp circuit then 10/3 would have been appropriate.

"And finally why is it called 220v if it's really 240v?
Who calls it 220v? Not me.
That is a generic term adopted by the masses.
Actually your oven is 120/240v, NOT simply 240v. There IS a difference.

Many code revsions ago the nominal voltages were added to the code. The nominal residential voltages are 120 V and 240 V. Both are RMS so the peak is higher by sqrt(2) = ~1.4
208 is most often seen as part of a 3 phase system, along with some other non-residential type voltage (high leg stingers, etc.)