Don't quote me on this. But I believe there is one carrier in China that is CDMA based. I don't know which carrier you used in China though.
Nah, not really anything to do with CDMA. Rather, one of the Chinese carriers use one of the TDD LTE bands (38-41) present in the Sprint/SIM-free/world version but not in the AT&T/T-Mobile/Verizon version.
To summarize:
SIM-free: Works on all four major US carriers without issue (whitelisted on both Verizon and Sprint; AT&T and T-Mobile have open networks)
Verizon: Comes unlocked from factory and works hassle-free on Verizon, AT&T and T-Mobile. Doesn't have the necessary LTE bands for Sprint and likely isn't whitelisted anyway.
Sprint: Locked to Sprint but can be unlocked once contractual obligations are fulfilled. Works on AT&T and T-Mobile once unlocked. Can also be used on Verizon if unlocked but since it's not on Verizon's whitelist, cannot be used to activate new service/SIM and some discounts (e.g. contract-free/EDGE $25 line discount) may not apply.
AT&T: Locked to AT&T but can be unlocked once contractual obligations are fulfilled. Works on T-Mobile once unlocked. Can also be used on Verizon if unlocked but since it's not on Verizon's whitelist, cannot be used to activate new service/SIM and some discounts (e.g. contract-free/EDGE $25 line discount) may not apply. Doesn't have the necessary LTE bands for Sprint and likely isn't whitelisted anyway.
T-Mobile (full price from Apple Store): Comes unlocked from factory and works hassle-free on AT&T and T-Mobile. Can also be used on Verizon if unlocked but since it's not on Verizon's whitelist, cannot be used to activate new service/SIM and some discounts (e.g. contract-free/EDGE $25 line discount) may not apply. Doesn't have the necessary LTE bands for Sprint and likely isn't whitelisted anyway.
T-Mobile (bought from T-Mobile or authorized dealer): Locked to T-Mobile but can be unlocked once contractual obligations are fulfilled. Works on AT&T once unlocked. Can also be used on Verizon if unlocked but since it's not on Verizon's whitelist, cannot be used to activate new service/SIM and some discounts (e.g. contract-free/EDGE $25 line discount) may not apply. Doesn't have the necessary LTE bands for Sprint and likely isn't whitelisted anyway.