I've found two sources that appear to provide easy to read explanation between Radiance vs. Irradiance and remote sensing reflectance and water leaving radiance.
Starting with Radiance vs. Irradiance:
Irradiance is simple: exchange of energy (in the form of photons) across a given area of flat surface per time. Radiance is more complicated: exchange of energy (in the form of photons) across a given area of flat surface per time and then divided by the amount of steradians from which the "given area" is collecting light.
The author uses two figures to discuss Radiance and Irradiance with respect to Illuminance.
Also, a good reference may be The Light Handbook provides additional information.
In terms of remote sensing reflectance and water leaving radiance
This comment here
Remote sensing reflectance (Rrs) contains the spectral colour information of the water body (below the sea surface). Rrs is the ratio between water-leaving radiance (Lw, above the sea surface) and downwelling irradiance (Ed, above the sea surface). Lw can be estimated from above-water radiometric measurements, in this case reflected skylight must be removed using a "surface reflectance factor" (rho).
Further comment: In ocean colour, often the term "water-leaving reflectance" (rho_w) is used instead of Rrs. The difference is: rho_w = pi*Rrs (with related change in units)
Illustration of light rays contributing to the irradiance reflectance
Illustration of light rays contributing to the remote-sensing reflectance