A residence permit, temporary, time limited or permanent is restricted to the country of issue. Ie you are allowed to work and live (Pay taxes) in the country that has issued you a residence permit. These permits have also different categories. Some are based on family relations such as marriage to an EU citizen or economic and or employment situation. In the latter case a residence permit could be issued based on your employment of a foreign company that chooses to base you in a European country for a longer term and you meet the residence criteria and not just those for a visa.
With a residence permit for family or other purposes you are not allowed to work for other than employers from the country of issue and you are restricted to 90 days within 180 in other schengen countries.
Lets say your spouse moves from say France, where your residence permit was issued to Germany, you would have to apply for a new residence permit in Germany and your spouse would have to be registered in Germany.
So basically the residence permit does not allow you to roam free and work for any airline or business in the union.
Quite familiar with the process as my better half holds a residence permit until meeting the requirements for a citizenship such as speaking the local language and 4 years of continuous residency.