The FMCSA Sticker is needed when crossing state lines because that type of inspection is a federal requirement. Federal inspections are somewhat stricter than state inspections. For example, with state inspections, you can pass even with a light oil leak, whereas roadside inspections done at state lines have resulted in drivers being written up for oil leaks.
State inspections are needed for truck registration in Texas. If you have Texas plates, you will need a state inspection; the DMV will not accept a Federal inspection. This is often a source of confusion for drivers.
Federal inspections come with a sticker and two copies of the inspection, one for the truck and one for the safety office. We get a lot of requests for copies of the inspection for their safety office. The driver should turn in the extra copy of the inspection to their safety office as soon as possible.