From the labor standpoint there is a huge difference. The Railway Labor Act of 1926 opens with definitions. A Carrier is a party to a labor agreement, an airline may or may not be. Labor, agreements are between parties. Parties are employee certified representatives and Carriers.
All of the provisions of subchapter I of this chapter except section 153 of this title are extended to and shall cover every common carrier by air engaged in interstate or foreign commerce, and every carrier by air transporting mail for or under contract with the United States Government, and every air pilot or other person who performs any work as an employee or subordinate official of such carrier or carriers, subject to its or their continuing authority to supervise and direct the manner of rendition of his service.
(May 20, 1926, ch. 347, § 201, as added Apr. 10, 1936, ch. 166, 49 Stat. 1189.)
Part 151: First. Duty of carriers and employees to settle disputes
It shall be the duty of all carriers, their officers, agents, and employees to exert every reasonable effort to make and maintain agreements concerning rates of pay, rules, and working conditions, and to settle all disputes, whether arising out of the application of such agreements or otherwise, in order to avoid any interruption to commerce or to the operation of any carrier growing out of any dispute between the carrier and the employees thereof.
Second. Consideration of disputes by representatives
All disputes between a carrier or carriers and its or their employees shall be considered, and, if possible, decided, with all expedition, in conference between representatives designated and authorized so to confer, respectively, by the carrier or carriers and by the employees thereof interested in the dispute.
Airline does not appear in the Railway Labor Act. The FAA grants certificates to an Air Carrier, not to an airline. An airline is a commercial business with marketing and all the other accoutrements of a commercial business. An Air Carrier is a thing defined by law, under certain regulations, FAR's etc, and constrained by those regulations.
This may seem like a trifling difference but the RLA is now 95 years old many different business models have been tried. The law only cares about Carriers. Operational authority is granted to Carriers and employee's have agreements with Carriers. In an extreme situation, the Administrator can remove or suspend the certificate of a Carrier.
Carriers have defined areas of operational control which has proven to be a problem for some types of joint ownership arrangements. Joint use agreements, Part 135, Part 91 subpart K, and other agreements have been used and the FAA is always concerned with "who has control", or "who is the certificate holder."