In this section the following words have the meanings indicated. “Bank or trust company” means: a commercial bank; a savings bank; a trust company; or a company that substantially competes with national banks in the State. “Savings and loan association” means a savings and loan association that: is organized under the laws of the State; is organized under the laws of another state and is admitted to do business in this State; or is organized under the laws of the United States and has an office in this State. Except as provided in subsection (c) of this section, personal property is not subject to valuation or to property tax, if the personal property: is owned by a bank or trust company or a savings and loan association and is used in connection with the processing of deposits or loans of the bank or trust company or savings and loan association; is a computer program, as defined in § 11-225(a) of the Tax - General Article, or computer hardware; and is not used in connection with word processing. The exemption under this section does not apply to any personal property that is leased, loaned, or made available by a bank or trust company or a savings and loan association for the use of a person that is not a bank or trust company or savings and loan association.