Trade Lines are a part of the TransUnion Full Credit report:

O - Open Account : An open account is an active loan or credit card.
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R - Revolving or Option : A revolving account is an account created by a lender to represent debts where the outstanding balance does not have to be paid in full every month by the borrower to the lender. Credit cards are a common example of a revolving account.

I - Installment : Installment accounts are those that have a fixed payment for a fixed period of time. A mortgage loan is an example of an installment loan.
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M - Mortgage : A mortgage account is a home loan.
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C - Check credit (line of credit) - A line of credit, abbreviated as LOC, is an arrangement between a financial institution, usually a bank, and a customer that establishes a maximum loan balance that the lender permits the borrower to access or maintain.

This is the subject who the background check was run on and their relationship to the account being examined.

A - Authorized user of shared account : Authorized users piggyback on the credit of a friend or relative. These users are entitled to use the credit extended to the cardholder, but have no legal responsibility to pay the bill.

C - Joint contractual liability : Joint account holders actually share ownership of the account and both are liable for repaying the debt. A joint account must be opened by the account holders at the same time.
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I - Individual account for sole use of customer : An account where the subject is the sole owner and no one else is liable or connected to that account.

M - Account for which subject is liable but co-signer has liability if the maker defaults : If the subject buys a vehicle but needs a co-signer on the account you would see this "M" code

P - Participant in shared account which cannot be distinguished as C or A : In these situations the borrower is joint on the account but the contractual liability can not be determined.
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S - Account for which subject is co-signer and becomes liable if maker defaults : In this case, the subject may have a friend or relative that purchased a vehicle and co-signed for the loan.

T - Relationship with account terminated : In this case the subject is no longer associated with the account

U - Undesignated : The account hasn't been designated yet, perhaps it's a recently opened account

X - Deceased : The subject has been reported as deceased