I have included the Apple LTE website link below.
iPhone - View countries with supported LTE networks - Apple
There are 5 types of iPhones.
Sprint, Verizon, & Sim-Free iPhones are the truly internationally unlocked iPhones. They all work the same basically.
Which basically means you can use all carriers, CDMA & GSM.
T-Mobile & AT&T iPhones are GSM Only. These you cannot use with Sprint/Verizon although the former you can use with T-mobile/At&t.
This will still work for many US/international carriers, with the exception of places like China, Hong Kong, Puerto Rico.
Only the Apple Store sells Sim-Free iPhones(Full Price will say unlocked on the receipt), but generally an iPhone activated through a plan will be an iPhone corresponding with that plan.
Ex. If you go to Sprint you will get a Sprint iPhone. T-mobile has T-mobile iPhones.
Unlocked means the phone is not tied(locked) to one number.
Financing generally ties your phone number to that android/iPhone, which will lock it until you complete the payments.
Only Apples Iphone Upgrade Program lets you have the phone not be tied to a number.
So if you're looking to buy an Internationally unlocked iPhone to use with any carrier, you must purchase a Sprint, Verizon, or Sim-Free iPhone. Reminder that this only applies if you want to use carriers on the Sprint, Verizon, or the list of CDMA carriers I have included in the link below. This rarely is applicable to many unless you are taking the phone to China, Sprint, or Verizon & you currently have a T-mobile or At&t One. Due to the fact the GSM iPhone works with almost 90% of carriers anyways.
I have included the Apple LTE website link below.
iPhone - View countries with supported LTE networks - Apple
Summing it up, if you are never going to use a Chinese, Hong Kong, Puerto Rico, Sprint, or Verizon Carrier, or plan to sell to someone with those carriers, then any iPhone is fine. If you pay it off, it will be unlocked.
If you need internationally unlocked Purchase a Sprint/Verizon/Sim-Free Iphone.
Otherwise T-mobile/At&t Iphones will work with most international carriers anyways.