To understand why the image from a projector is much bigger than the image in a camera, you need to be aware of how the lens used in a projector varies from that of a camera. It is the difference in the lens and its working principle that makes the image either magnified or reduced in size.
Convex lens
So the lens used in a projector is the convex lens also called the converging lens. It is the magnifying lens and is curved outwards on both sides.
What is the convex lens?
A convex lens is a lens that bulges outward in the middle. This type of lens is used for convergent light rays, which means that the parallel rays of light will converge (meet) at a single point after passing through the lens. When light passes through it, you get an image on the screen larger in size compared to the size of the object and the image is inverted.
Why does a projector use this lens?
There are several reasons why a projector uses a convex lens. First, a convex lens can converge the light rays from a wide area onto a small area. Second, a convex lens can magnify objects. Both are important because the projector’s bulb is usually small but the screen is usually large. Lastly, a convex lens can reduce aberrations. Aberrations are the distortions of the image caused by the imperfections of the lens. By using a convex lens, these aberrations can be minimized.
How to define the kind of image you get from a projector?
A projector produces a real, inverted, and magnified image (as discussed above).
Real image
A real image is an image formed by actual rays of light. Real images are always inverted, and they may be either larger or smaller than the object.
Virtual images
An image, that is seen in a mirror, in which the rays of light appear to be emanating from some object that is not there is called a virtual image. Virtual images are always erect. They, also, may be either larger or smaller than the object.
Conclusion
A slide projector produces a real, inverted, and magnified image. The image must be real because otherwise, you would not be able to project it onto a screen. The image is inverted, so the slides have to be put upside down. A projector uses a convex lens just as the magnifying glass also uses a convex lens (already explained). The image is upright, magnified, and virtual. The object must be at or within the focal length of the lens. I think that is enough info to answer your question.
