The larger the lens diameter, the faster the lens is, in a general sense. Faster means admitting more light for a given shutter speed.
Maximum aperture or lens speed, is stated as an f-stop, f/2.8 being common for today's digital point and shoot cameras unzoomed to the widest angle. The smaller the f-stop number, the more light is admitted; the larger the opening in the lens iris relative to the focal length.
"Millimeter Lens" also refers to focal length which has to do with wide angle versus telephoto versus zoom representing field of view. Digital cameras may or may not be described with a 35 mm film camera equivalent for focal length. The only easy way to compare apples with apples is when both cameras you are comparing have focal length stated in 35mm film camera equivalents. Standard angle for most point and shoot cameras made in the last 30 years is between 35 and 38 mm focal length in 35mm film camera equivalent. Traditional 35mm film and larger format film cameras use 50mm lenses as standard angle whereby 35mm lenses are considred wide angle. The typical point and shoot 3x zoom camera goes up to about 105 to 110mm focal length, 4x zoom goes up to about 140 to 150mm focal length (35mm film camera equivalent).
Regardless of the focal length, f/2.8 always means the same amount of light admitted for a given shutter speed, f/4 always means the same amount of light for a given shutter speed, etc. But as the zoom is changed (the focal length is changed) and the lens iris opening stays the same in absolute diameter, the f/stop will change, admitting less light as zoom is increased. A typical camera with an f/2.8 lens and 3x zoom will have at most about f/4.5 in terms of light admittance when zoomed to the maximum.
Approximate focal length versus field of view:
28mm -- 65 degrees side to side
38mm -- 50 degrees
50mm -- 40 degrees
70mm (typical 2x zoom) -- 30 degrees
105mm (typical 3x zoom) -- 20 degrees
140mm (typical 4x zoom) -- 15 degrees
(What is 2x, etc. zoom varies with the widest angle provided on the camera)