Short answer: a cover-up hides an old tattoo under a new design, and laser removal fades or removes it. Often the two go together: a few laser sessions lighten the old tattoo, and then the new design goes on top. The right choice depends on the old tattoo and on the design you want.
What a cover-up is
In a cover-up, a new design is tattooed over the old one. To hide the old tattoo, the new design is usually larger and darker than the old one, so the choice of motif is more limited than on clean skin.
When it makes sense to lighten the old tattoo first
If the old tattoo is dark or dense, or you want a light and delicate new design, a few laser sessions first can give the artist much more freedom. Gall works with both on one site, so the two steps are planned together. More about the procedure: laser tattoo removal in Lyubimets.
Laser clinics describe it this way: light lightening usually takes about 1 to 3 sessions, and a denser tattoo with a lighter or more detailed new design can take 3 to 6. The goal is a workable base, not necessarily full removal, and the skin should be allowed to settle for several weeks after the last session before the cover-up is tattooed. Removal first is especially worth considering when the old tattoo is very dark or saturated, the lines are blurred or badly drawn, or the new design is light or minimalist. A direct cover-up can work when the old tattoo is small and light, although the new design may still need to be adapted.
When laser removal alone is the answer
If you simply do not want the tattoo any more, full removal is the way. It takes several sessions: read how many sessions laser tattoo removal takes.
What it costs
The price of a cover-up is very relative: it depends on whether it is only a refresh of an existing tattoo or an entirely new design, and hand-drawing plays a big role. Laser removal is priced by size and number of sessions. Read how much a tattoo costs and how much laser removal costs.
How to decide
Send a photo of the old tattoo, its approximate size, and what you would like instead through the inquiry form. At the consultation the tattoo and the skin are assessed, and you get a plan: full removal, lightening for a cover-up, or a cover-up straight away.
Source for the session numbers: Ray Studios, a tattoo-removal clinic. This is a clinic guide, so treat the numbers as typical, not as a promise.