Those are two poor definitions, over simple.
The following (from Wikipedia) is a good stab......
A professional is a worker required to possess a large body of knowledge derived from extensive academic study (usually tertiary), with the training almost always formalized.
Professions are at least to a degree self-regulating, in that they control the training and evaluation processes that admit new persons to the field, and in judging whether the work done by their members is up to standard. This differs from other kinds of work where regulation (if considered necessary) is imposed by the state, or where official quality standards are often lacking. Professions have some historical links to Guilds in these regards.
Professionals usually have autonomy in the workplace - they are expected to utilize their independent judgement and professional ethics in carrying out their responsibilities.
This holds true even if they are employees instead of working on their own.
Typically a professional provides a service (in exchange for payment or salary), in accordance with established protocols for licensing, ethics, procedures, standards of service and training / certification.