A scalpel is the classical name in English for pretty much anything makes an incision.
Surgical sharpness is just sharp enough for surgery and sharp enough to cause no harm by being too blunt and cheap enough to be disposable. These days more and more scalpels are made of plastic with a permanently mounted blade attached. Then the whole thing is disposed of. There are many types of scalpel blades that vary in length, width, length of cutting surface and overall shape. There is a scalpel made for just about any of the hundreds of different situations that various types of surgeries present.
You would use different instruments to cut different materials, right? A saw if you are cutting a piece of wood, a serrated knife to slice bread, and a carving knife to cut up turkey. Same thing goes in surgery.
If the goal is to make a deep, but narrow “stab” incision in skin (for instance to insert a 5mm laparoscopic trocar through the abdominal wall) then a blade that is long, narrow and comes to a point (#11 blade) is perfect. If one needs to make a deep, long incision like a skin incision in an obese patient then a wide, positively curved scalpel (#22) works well. If the surgeon has to be a little more delicate or has to make a curving incision with a narrow radius, then a blade that is narrower and has a smaller cutting surface (#15) is great. Different situations calls for different sharpness and depth of incision.
Normally now in surgery it is a disposable steel blade attached to a sterilizable handle. The handles and the blades come in various sizes and some handles are bent for convince.
The term scalpel might also be used as a non steel cutting device as electrical scalpel or for just plain esoterica obsidian scalpel. It is a nonspecific term.
The “skin-knife” makes one cut then is taken off the surgical Mayo stand & never used again. Other scalpel handles with replaceable blades are used. A blade used internally may even be replaced as the surgery goes along. There are a number of different blade shapes for doing different tasks and are referred to by that number when requesting a fresh scalpel for a different task.
A #10 scalpel blade is a very common slightly curved cutting edge.
The two most commonly used scalpel blades are a #15 and a #10. A 10 blade is larger - a 15 blade is smaller. Both are called scalpel blades.
Scalpel is a combo of blade and blade handle which is not separable.
Now a days both are different part and 10 # blade is a type of surgical blade used with handle during surgeries.
Blades are disposable. Only handles are reusable and even that is not always the case. So a scalpel blade is used only once. During one surgery, the blade may be changed if it becomes dull in the process. It's true that the scalpel used to be wholly reusable when the blade was part of it.