If you want a quiet, convenient way to power your lights, your idea of using an DC/AC inverter with a conventional 12V lead-acid battery is probably the best one. You will not be able to supply 200W in a cost-effective way using either AA batteries or a miniature portable 'power bank' for cell phones.
Doing some figures, using an approximate energy density of 35 Wh/kg and a battery mass of around 20kg, this gives you a total capacity from a single automotive-sized battery of 700 Wh. You will need to verify this capacity when you choose a battery, which may be difficult since many automotive batteries do not have watt-hour or amp-hour ratings advertised. However, this means you can meet your requirement (ca. 400 Wh) with a single (fairly expensive, but reusable) battery connected to an appropriately rated inverter. Since you will be operating the battery without immediately charging it, look for a deep-cycle type battery with a discharge count rating in addition to its energy capacity rating.
Another option which is louder and requires a different investment is a hydrocarbon-fueled generator. These are available in a variety of capacities and fuel capabilities. Many options would greatly exceed your duration requirement, but would still be usable. Be aware of the exhaust of the generator and only operate it outdoors with enough ventilation.
To be honest I'm surprised they were that similar. Putting two bulbs in series has some strange effects that can be confusing when you first see them.
No two lamps are going to be identical, one will be a tiny bit higher resistance than the other.
Current is the same in both lamps and power = resistance * current which means one of the lamps will have a very very slightly higher power dissipation.
This is where the weird stuff starts to happen.
Power dissipation in a lamp = heat.
The resistance of (most) metals increases with temperature.
So the slightly higher resistance lamp has a slightly higher power which means it gets slightly hotter. If it gets hotter it's resistance will increase more. Which means the difference in resistance increases and a higher proportion of the power goes into that one lamp. You get a positive feedback effect, the lamp with the higher resistance ends up significantly brighter, far more than you would expect based on their resistance differences when cold.
You can check this easily:
You measured the voltage and current for each lamp when they were on. That means you can calculate their on resistance. Use a meter to measure the resistance of them when they are out of the circuit and cold, you'll get a very different number.
Best Answer
Christmas lights don't exactly "share" the same voltage on each lamp - they happen to have approximately the same voltage but that is because they are all in series and have roughly the same impedance to current when glowing.
If your supply is 240V ac and you have 20 lamps in series, each one will have approximately 12V across the lamp terminals. It makes sense for each lamp therefore to be rated for 12V operation and of course if you tried to put that across 240V it would instantly fail and blow.
If you took a 240V lamp and put it in series with another 240V lamp, each lamp would be receiving 120V and therefore the brightness would approximately reduce by a factor of four.