What is the difference between the different camera speeds?

None, it really doesn't work like that. There are four aspects of a camera that determine the final picture. They are Camera Speed, Apeture, film ISO, and available light. All of these are connected so that not one of them works independantly of the other. There is no combination of all four that will yield an acceptable image in daylight and nighttime without adding a flash unit (adding available light).

The difference is that, for example, 1/250 is half as fast as 1/500 etc. They are the fractions of a second for which the camera shutter is open. There is no one 'best' speed. You will require longer speeds at night, and your camera on a tripod, in order that more light might reach the lens. In daytime you want a speed at which you can hold the camera without there being 'camera shake' apparent. Roughly that is that the minimum speed at which you should hand hold is the focal length of the lens. So a lens of 200mm should not be handheld at below 1/250. But speed also needs to be combined with aperture and is also dependant on what you are photographing. A small aperture, perhaps, with a long speed for landscapes, a larger aperture with a fast speed for action.

Each shutter speed lets in 2x the light (going from 1 1000 sec to 1 sec. Need slow speed for night and high speed for daylight or action

Camera speeds indicate how long the camera's shutter is open during the taking of a picture. Best exposure depends upon the subject you are shooting and the lighting involved. Also if the subject is in motion that too can be a factor...

If you mean film speeds, Kodak Max fim is 800 speed. Meaning it is going to be grainy. But will work good for indoor or low light shots. I would use 200 speed for candid shots. if you use 100 you might need a tripod. The higher the film number the less light needed. Although the quality of the image decreases slightly with higher speeds.

on a slr film camera about 1/30 sec

if digital adjust to 800 or hight asa setings