There are a number of confusing terms in the Medical Esthetics field, and I hope this guide will help you decide which one is best for you.
Esthetics: a branch of philosophy dealing with the nature of art, beauty, and taste, with the creation and appreciation of beauty.
Skin care: the range of practices that support skin integrity including nutrition, avoidance of excessive sun exposure, and appropriate use of emollients; that enhance appearance such as use of cosmetics, botulinum, exfoliation, fillers, laser resurfacing, microdermabrasion, peels, retinol therapy; and that remediate skin break down and relieve skin conditions.
Skin care is a routine daily procedure in many settings, such as skin that is either too dry or too moist, and prevention of dermatitis and prevention of skin injuries.
Skin analysis: analysis of any particular skin condition is made by gathering pertinent information regarding the presenting skin condition, including the location (face), symptom, duration, arrangement, morphology, and colour.
Cosmeceutical: are cosmetic products with bioactive ingredients purported to have medical or drug-like benefits. It applies only to products applied topically, such as creams, lotions and ointments.
All definitions were taken from Wikipedia.