Thrush,

Composite it not really a cable per say, it's a standard for transmitting video over a cable. The cable that carries the composite signal in the picture above is the yellow one, the red and white ones carry audio.

It is not a good connection from a picture quality point of view, if your DVD/TV support better then you should try and switch to something better.

As for scart-scart, again, it depends on your kit.
Scart is capable of transferring composite, s-video and RGB all in one cable (scart is actually 21 cables inside if fully wired).

If your DVD supports RGB output and your tv supports RGB input, both over scart, then this is what you should use. Audio will also be carried by the scart connection.

Otherwise, if your TV supports s-Video over scart, then you should be able to use this too.

You need to have a look at both your TV and DVD's manuals to figure out what you can or can't do.
Note: You MUST use a fully wired scart cable, some have unconnected pins

Good luck.