Dan (Dpea);
Most companies pay by the weight of the load or required cargo area. Your truck is a "D" unit by GVW and length. Granted it may not be able to move all "D" loads offered to you, BUT it is a "D" truck under most definitions.
Many companies will offer to "D" units loads that are not "D" loads to keep them moving. For example, you take a "D" load at the full rate ($1.20 $1.30 - whatever your carrier pays, plus fuel surcharge) to Dallas Texas. You unload in Texas and the (carrier)company is given a cargo van load to let's say "Idaho", but has no cargo vans in Dallas, I'm sure the carrier would offer it to you since you are the vehicle they have in Dallas. That load would generally pay the cargo van rate (.70, .80 or .90 cents per loaded mile plus fuel surcharge).
Likewise, even if your truck is classified as a "C" unit by your company, the company probably pays "D" rates for any load over 5,000 pounds. So if you are offered a load that weighs 11,500 pounds, you would be paid the "D" rate.
The same is true with length or cargo area. A Sprinter van is sometimes paid a "C" rate because the dimensions of the load would not fit in the normal cargo van (ie. load 11'8" long).
I would not let the company's classification of your vehicle scare you away from them. Just watch to make sure you are not being passed over on "D" loads you are able to haul.
I hope this explains your situation better for you.
Thank you,
HotFr8Recruiter.