Hi Olga - that's a really good question, especially since commitment and loyalty seem so close in meaning.
Commitment is an agreement or pledge to do something in the future. The commitment might be obligatory or emotionally motivated.
Loyalty is unwavering allegiance, which is oftentimes motivated by faithfulness to an entity (government, religion, etc.), a person, ideal, custom or institution.
The important thing here is that loyalty is motivated by a sense of faithfulness. In that way, being loyal to something is a much stronger feeling that being committed to something.
If an employee is described as being committed to the company, it probably means that the employee shares the same goals as the company, performs good work and is generally a good team-player.
By contrast, if an employee is described as being loyal, it probably means that the employee is entirely devoted to the company and would do just about anything for the good of the company. If an employee is truly loyal, he or she would not seek employment elsewhere.
In sum, describing something as loyal is much stronger than describing it as committed.
Hope this helps!