Yes and no. Permanent makeup is tattooing as the basic principles of traditional tattooing and cosmetic tattooing have many similarities. However, the face is different than the body. While tattooing on the face it’s necessary to go a bit shallower than the body in order to avoid damage to the skin and pigment migration, especially for the the eyelids which are the thinnest skin on the face. The eyebrows, meanwhile, are the highest point of face and exposed to a lot sun and skin care products. And because the lips are muscle tissue with tremendous blood flow, color implanted in this area should expect to heal softer.
The face also exfoliates at a faster rate than the body and generally is exposed to more sun and skin care products. Also we typically do not cover over our faces as we do with our bodies.
Next, different kinds of color formulations are used. So for the face only formulations of cosmetic pigment should be used and not faster-spreading ink whose particles are smaller. The spectrum is also comprised mostly of tertiary colors and not straight primary colors that can last a lot longer under the skin.
And finally to keep in mind, the darker and more saturated the color the longer it will resist fading. The lighter the color and saturation, the faster it will fade. This means that clients who have dark hair who request a “very light and natural-looking brow or eyeliner” should expect their work to fade more quickly even though a dark pigment color was used.