Regardless of what the dictionary says the words mean, nowadays the word "fidelity" is primarily used in only two contexts: 1) sexual fidelity, i.e. maintaining a monogamous relationship with a single partner, not "cheating" on them; 2) high quality sound reproduction, often in the phrase "high fidelity."
I would be cautious about using the word "fidelity" in marketing communications. This is true despite the fact that some financial companies, banks, and so forth use the word as part of their names, notably the US firm "Fidelity Investments."
"Loyalty" is much commoner, and a much safer choice. People often talk about "customer loyalty" to a brand, never about "customer fidelity." "Loyalty" is much wider, and refers to all kinds of support. It is often used to refer to devotion in the context of business or military relationships. It sounds natural to say "Steve had been in the Marines and had a strong sense of loyalty to the United States Marine Corps." It sounds strange and comical to say "Steve had a strong sense of fidelity to the United States Marine Corps." (This is true, despite the fact that the US Marine Corp motto is "Semper Fidelis!" The word "fidelity" is derived from the Latin "fidelis," and the motto means "always faithful.")