Yes both sprint and Verizon phones all have sim cards. And as mentioned earlier some phones have removable sims and others don't.
With the phones that have non removable sims, they are soldered to the main board and linked to the imei. Force removing it will turn your phone into a paperweight.
With the phones that have removable sims, on Verizon most are sold internationally unlocked, but not domestic. And on sprint they are sold completely locked, with the owner being able to request an unlock for international use only after 90 days of having your account in good standing.
Within the next year or so, both sprint and Verizon will be switching to removable sims only, probably for modernization purposes. Not to mention the possibility of OEMS now selling phones with bands for all networks, like the HTC one.
I hope that cleared things up.
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