Lumens, candela and lux describe different aspects of a dive light's output. Understanding the difference helps explain why two lights with the same lumen rating can look very different underwater.
Lumens (lm) measure luminous flux: the total visible light output, weighted for the sensitivity of the human eye. A lumen rating alone does not tell you how tightly that light is focused.
Candela (cd) measures luminous intensity in a particular direction. A narrow beam can concentrate its output into a bright central spot, while a wide beam spreads its output over a larger area. Two lights with equal lumen ratings can therefore have very different peak candela ratings. One thousand millicandela (mcd) equals one candela.
Lux (lx) measures illuminance: the light reaching a surface per unit area. One lux equals one lumen per square meter. A lux measurement is meaningful only with the measurement conditions, including distance and position within the beam.
There is no single conversion between candela and lumens without knowing the beam's intensity distribution. For a uniform beam, lumens equal candela multiplied by the beam's solid angle in steradians; real beams usually have a central hotspot and surrounding spill with different intensities.
For divers: compare beam pattern and usable runtime as well as lumen output. A concentrated beam is useful for signaling, while a broad, even beam is useful for lighting a camera's field of view. Water clarity and scattering also affect what you actually see, so a higher lumen rating does not automatically mean better visibility.