Pure vs modified sine

I fully grasp the difference.
The question:
In the 3-500ish range (planning for a small fridge), will it make a difference??
Fridge 200 buk walmart special.
What specific items won't like the (1/3 of the price) modified??
Eg: laptop...it won't like running on it, but would it charge okay when turned off?
Charger for my drill batteries?

Fridge will like pure better than modified. If it has an AC motor compressor it will run but the modified sine wave will cause it to run hotter. If it's an inverter design, and given that it seems the USA doesn't care about household PFC (!), it will likely work just fine. If it's an inverter design destined for Europe/AU/NZ etc you may find it doesn't like the modified sine wave since the PFC (power factor correction) circuits may get upset seeing the modified sine wave.

The laptop AC adapter is likewise. If it has no PFC or passive, it'll work fine. If it has active PFC it may not.

Drill charger, probably doesn't have any PFC so will work.

Unfortunately it's not easy to tell what has PFC at all, let alone active PFC so pure sine is usually the best choice but if you want to spin the wheel things might work without trouble, but typically the things you are powering won't blow up as a result if they don't.

What is power factor correction?

I used to install " modified sine wave " inverters before sine wave technology was common. The items that used to blow up on the
these were small plug in power supplies for devices etc, and some fans. Also stereo systems used to have an annoying buzz.
The other thing ,a generator needed three times the nominal power to get full charging capability due to peak clamping. Before we knew that, we got disappointing results on smaller boats with smaller generators.

Most of today's electronics don't mind modified sine wave inverters.. But they are a no-go for anything with a motor.

Any electronics with a power circuit (Toaster, microwave, oven, heating blanket, etc) will usually run at a lower power rate on the modified inverters.

Stick to pure sign wave.. fewer problems.

I tried my inexpensive, relatively low-tech refrigerator on my older 1500W Xantrex X-Power inverter and it ran, but the compressor was noticeably hotter to the touch than when running on the grid, so I only did it for a few days as a test. I'm not sure a 3-500W MSW inverter would even start the compressor on my fridge, even though it only sips about 80w when running. The fridge runs great on my 1200W PSW inverter without running hotter.