OP-1 is a form motor carriers use to register with the Federal Motor Carrier Safety Administration (FMCSA) for operating authority. MCS- 150 is form to register for a USDOT number. Many companies will have filled out both forms. If you are an attorney handling a tractor trailer collision case, make sure you send a Freedom of Information Act requests request for both. They both include a spot for the carrier to sign that it is familiar with Federal Motor Carrier Safety Regulations. The forms contain other useful information such as commodities carried.
The states of Alabama, Alaska, Arizona, Colorado, Connecticut, Florida, Georgia, Indiana, Iowa, Kansas, Kentucky, Maine, Maryland, Michigan, Minnesota, Missouri, Montana, New York, Nebraska, North Carolina, Ohio, Oklahoma, Oregon, Pennsylvania, South Carolina, Tennessee, Texas, Utah, Washington, West Virginia, Wisconsin, and Wyoming require MCS-150 registration of commercial vehicles even when intrastate. All carriers will have MCS-150s, but not all will have OP-1s (for example, a private carrier). Brokers and freight forwarder will have an OP-1 but not an MCS-150.
Hazardous material haulers fill out an MCS-150B; all other carriers fill out an MCS-150. Brokers and for hire carriers hauling property fill out an OP-1. For-hire passenger carriers must fill out an OP-1(P). Freight forwarders fill out an OP-1(FF). OP-1(MX) refers to a Mexican carrier and OP-1(NNA) refers to a non-North American Carrier.
Here is a chart from the FMCSA that explains what company must fill out what form.