That difference is in how they produce their colours.
All projectors produce colour by delivering tiny red, green and blue dots. These are the real primary colours (unlike the art-class ones of red, blue and yellow). Run all three colours in the right proportions and you produce white. Mix the proportions and you get a range of colours (called a 'gamut') that approximates quite well the colour range of the human eye.
The difference in the projection systems, though, is that while CRT, LCD and LCOS projectors produce all three colours at the same time, DLP projectors produce them in sequence, one after the other.
Of course, you don't see them appearing one after the other. The hundreds of thousands of microscopic mirrors on the Digital Micromirror Device (DMD) which powers DLP projectors, flicker to and fro thousands of times per second. A spinning colour wheel, with red, green and blue colour filters, is synchronised with these flipping mirrors, so that each produces the right colour light at the right time. Your eyes' persistence of vision smooths things out, so there is no flicker at all. But a side effect is the common DLP 'Rainbow Effect', where you catch flashes of colour in your peripheral vision. This is an optical illusion caused by the red, green and blue pictures being delivered in sequence, rather than simultaneously.
CRT, LCD and LCOS projectors don't produce a rainbow effect because they don't use a spinning colour wheel. That's because each of these is like three projectors in one. Each handles the red, green and blue colours quite separately.
This is most obvious with the CRT (Cathode Ray Tube) projector, in which you can see the three large coloured lenses poking out from the front of the projector. In this case the three colours actually travel three different paths through the air, meeting and merging only on the screen itself (assuming that the projector has been correctly aligned of course). The three colours overwrite each other on their scan lines, producing yellows and magentas and puces.
But a similar process happens inside LCD (Liquid Crystal Display) and LCOS (Liquid Crystal on Silicon) projectors. LCDs, you will recall, are semi-transparent panels than can change the opacity of each of their tiny pixels according to signal. LCOS, by contrast, changes its reflectivity. Because the light is bouncing off its surface, rather than shining through it, the control electronics sit behind the panel rather than around the edges of each pixel. This makes for a smoother picture because the black borders around each pixel on the screen are much thinner.
Both LCD and LCOS projectors use just one lamp which produces white light. But this is shone through three 'dichroic' filter/mirrors. One just lets the blue light through, reflecting the rest. The next two repeat the process for green and red light.
Each of the three resulting colour light beams is then fired through (for LCD) or reflected from (for LCOS) its own panel. The three colour beams, each now bearing their respective colour loads from the image being projected, are combined again and then focused through the projectors lens. As with CRTs the beams have to be aligned, but because all this is internal, it is done with great precision in the factory.
There's no reason why DLP projectors can't also use three DMDs and eliminate the rainbow effect. Indeed, already the InFocus ScreenPlay 777 is available. This uses three top-of-the-line HD2 DMDs and so eliminates the need for a colour wheel. But the problem is that it costs $49,999!
I can confidently predict that relatively affordable DLP projectors will, one day, be free of the rainbow effect. But that day will be when the patents run out. For the moment Texas Instruments is the holder of those patents and the creator of all currently available DMDs. When they've expired, then we can expect many other companies to join the fray, competitive capitalism to impose its mark, and perhaps we'll then get three-DMD DLP projectors down below $5,000.