Two names, one line
The window and the price list disagree, and the price list wins.
Foot Reflexology is painted on the storefront glass. Foot Massage is the line on the price list, at 30 or 60 minutes. There's nothing in between — one foot appointment, and either name gets you the same reclining chair and the same therapist working the same soles.
Most places sell the two words as separate products with separate price tags: a foot rub for people who want their feet to feel better, and reflexology for people who want something more. With one foot line, we can't run that argument even if we wanted to. You're buying time on the feet. The rest is vocabulary.
Use either word at the desk and you'll be understood. Your therapist can work the whole sole in a set order, or go straight to the heel that's been complaining and stay there — both sit inside the same booking. If one of those is what you came for, say so in the first minute.