Using iPhone SIM in an iPad?
It depends on the carrier. Generally, iPad SIMs from a carrier are so-called ‘data SIMs’ as they only provide the data service. A normal SIM can act as data SIM if the carrier supports it with an appropriate carrier bundle. You can speak to your carrier or see if anyone else has asked your carrier on a forum, e.g. UK's EE. That chat with Verizon appears like you're talking to a misinformed person — the SIM will easily fit, and the size difference of the iPad itself is obviously not a concern.