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The lux will describe the range of the beam, the lumens the total output.
A light with low lux but high lumens would be like a light bulb, a glow of light in a flood pattern...reducing or eliminating a hot spot.
A light with high lux but low lumens might be like a laser pointer...nothing but a bright hotspot...but little to no flood.
Those are more extreme examples, but they illustrate the difference. You can then describe the beam pattern that interests you.