The Railway Labor Act (RLA) is a federal law that was passed in 1926 to govern labor relations in the railroad industry, and amended in 1936 to include the airline industry. It's a tool that's used for more collective bargaining, arbitration, and strikes within the member industries. Under its auspices, employees have more rights and more protection. http://www.en.wikipedia.org/wiki/Railway_Labor_Act
The National Labor Relations Act (NLRA), often called the Wagner Act, was passed as a federal law in 1935 as a means for employees to have more bargaining power by creating labor unions. It does not apply to employees covered by the RLA, upper level management of agricultural and domestic firms, all federal, state, or local government employees, and the owners of independent contracting firms. It's more for the lower eschelons of the private sector (such as blue collar laborers). It came about after the Great Depression when so many people were affected by unemployment. http://en.wikipedia.org/wiki/NLRA
Now, the Federal Labor Relations Authority (FLRA) has nothing to do with either the RLA or the NLRA. It's an independent agency within the United States government that mediates between it and its own employees. http://en.wikipedia.org/wiki/Federal_Labor_Relations_Authority
The only similarity I find between all three of them is that they were all set up by the U. S. government, and they all help employees have more rights and get better benefits from their employers.