1. What is difference between international unlocked and US factory unlocked smartphones?
what is international version cell phone : they are usually allowed to work with any SIM card in the world, except domestic SIM cards other than the one from the original network carrier of the phone. Factory unlocked phones can be used anywhere they came unlocked from the factory and don't have any network restrictions. If one needs to unlock a phone there are several ways:
You can ask your current carrier to unlock it.
The law says they are obliged to do it, but the bad thing is that your phone must NOT be under contract.
You can go to repair shop. They will unlock your phone by cable using a special software. The bad thing is that you have to leave your phone there for a few hours.
You can use a third party phone unlocking service like. They will search and provide you with an genuine unlock code from the manufacturer's database. This is the safest method to unlock any phone.

2. They're the exact same thing
They're the exact same thing. If the phone is unlocked, that means you can use it with any GSM carrier in the world. If you want to unlock your phone, you basically have 3 options:
Go to your carrier and ask them to unlock it. They're obliged to do so, they just don't advertise it. The downside is you'll probably have to wait for your contract to expire.
2. Go to a local phone repair shop. You'll leave your phone with them for a few hours or a day, and they'll permanently unlock it. The downside is that they use hardware to do so, and might damage your phone.

3. In most cases, it does mean the same thing - unlock is unlocked in other words can be
used on any network around the world.
Strictly speaking though, "factory unlocked" means that it is unlocked out of the box –
you buy it at full price and you buy it unlocked.
"Internationally unlocked" means it may be carrier locked in the country where you purchased your
iPhone but unlocked for use oversees.
To my knowledge this is rarely the case since most carriers
are well aware that some people can take their subsidized phones
abroad so they either lock it or
unlock it for any network - domestic or international.
Now, let's dig a little deeper here. Some carriers like Sprint will unlock
your locked phone only for international use so it will not work on
carriers within the U.S. At&t on the other hand will unlock it
for any network if you are eligible for unlock including for U.S.
domestic networks.

4. They are essentially the same with minor differences:
Internationally Unlocked Phones are unlocked from a service provider that it was previously locked to. This sometimes means the phone is unlocked for international use but is not eligible to be used on other US GSM carriers.
Factory Unlocked Phones are not made for a specific carrier thus are unlocked out the factory. These phones can be used on ANY GSM carrier as long as the phone carriers the band widths that carrier supports.