This will GREATLY oversimply things, but here is some insight:

-- "Government airfares" are the result of contract negotiations between the Government and airlines. These "contract fares" can only be used for Official Business. Period. Any other use violates the terms of the contract. ("Matching fares" are another level of complication I won't get in to, but basically they too are only for Official Business.)

Historically, "Goverment hotel rates" are NOT based on contracts. They are the result of a hotel deciding to offer rooms at a rate that is within the local "allowable Government per diem rate" (the maximum that the Goverment will reimburse an employee for a hotel room in a given geographical area). There is no contract; the hotel is free to offer (or not offer) such rates, capacity-control them, establish any other associated policy they wish (e.g., only for official business or for personal stays as well), etc.

[The Government has started to negotiate actual contracts with some hotels in certain cities, but this was just started in the past few years. If the hotel's Government rate is the result of a contract, then how the rate can be used will be subject to the terms of the specific contract.]