A camera lens gathers and concentrates sunlight exactly the way a telescope does, so it needs the same kind of filter in the same place: over the front, sized to the lens, fitted so it cannot be knocked off. The differences are practical rather than optical.
Sizing and fitting matter more than on a telescope
A telescope filter sits in a cell that grips the tube. A camera filter usually threads into the front of the lens, and a lens that extends while zooming or focusing can shift a filter that is not properly seated. Check the fit before you point the camera at the sun, and check it again after any change of focal length, because a filter that comes loose mid-exposure exposes both the sensor and, through the viewfinder, the eye.
Never use an optical viewfinder without the filter fitted
A digital single lens reflex sends the full concentrated image to your eye through the viewfinder. With a front filter fitted that is safe; without one it is the same injury as looking through an unfiltered telescope. Live view on the rear screen removes the risk to the eye entirely, though it does not protect the sensor, which will also be damaged by concentrated sunlight.
What the filter does to the exposure
A white light solar filter cuts the visible light by roughly a factor of a hundred thousand, which brings the sun into an ordinary exposure range: short shutter speeds at moderate apertures and base sensitivity. The practical consequence is that solar photography is one of the few kinds of astrophotography that needs no tracking, no long exposures and no dark sky.
Questions people ask about solar filter
Is a camera solar filter the same as a telescope one?
Optically yes, mechanically no. The filter material is the same; the mounting is sized and secured differently, and a zoom lens that moves needs more care than a fixed telescope tube.
Can I use a neutral density filter instead?
No. Photographic neutral density filters are designed to cut visible light for exposure control and are not specified to block infrared, which is the part that causes injury and sensor damage.
Does my camera need protecting too?
Yes. Concentrated sunlight will damage a sensor as readily as a retina. The front filter protects both, which is another reason it belongs at the front rather than anywhere else in the path.