Luminous intensity and luminous flux follow similar derivations.
Therefore, when concerned with regulating illuminance uniformity, it is more relevant to address intensity than luminous flux.
Luminaire luminous flux can be directed upwards and/or downwards reaching working surface directly or indirectly.
Illuminance means the density of the luminous flux incident on a surface.
The ratio of luminous flux to power input of a lamp.
British Dictionary definitions for luminous flux
a measure of the rate of flow of luminous energy, evaluated according to its ability to produce a visual sensation. For a monochromatic light it is the radiant flux multiplied by the spectral luminous efficiency of the light. It is measured in lumens Φv