Is there a difference between having a movable and non-moving breast lump at the age of 15 in terms of cancer?

Yes. Generally, a non-movable lump indicates inflammation around it. That means that the body's immune system has recognized it as "foreign." any lump of concern to you, moveable or not, should be checked out by your doctor. Sometimes, it's only normal anatomy that you're feeling. Btw, congratulations for doing self breast examination. If you don't know what that is, discuss it with your doctor.
Get it checked out. All breast lumps should be evaluated to insure that there is nothing to worry about. Mobility of a nodule (by itself) does not discriminate between benign and malignant. Your physician should be able to help you sort things out.
See your physician. Nonmovable lumps typically suggest pathology, see your physician, get the lump checked out. At age 15 chances are it is something treatable like an infection.