I know that radiance is expressed as $$[\text{radiance}] = \frac{\rm W}{\rm {sr} \cdot m^2}$$
and
$$[\text{irradiance}] = \frac{\rm W}{\rm m^2}$$
but what is the relation between these two quantities? Is irradiance commonly used to referring to power reflected on a surface? And radiance from a direct source?
As you stated, both radiometry units seem to be similar. While irradiance refers to incoming power, the radiance is used for two cases:
E.g. radiance in direction of the optical axis of a LED is higher, than its radiance at an angle of 15°. Optical simulations / ray tracing calculate the irradiance on surfaces. Your last two questions are mainly correct. However I would rephrase the first statement: Irradiance commonly is used referring to power incident on a surface.
rradiance is the power of electromagnetic radiation per unit area (radiative flux) incident on a surface. Radiant emittance or radiant exitance is the power per unit area radiated by a surface. The SI units for all of these quantities are watts per square meter (W/m$^2$), while the cgs units are ergs per square centimeter per second (erg/cm$^2$/s, often used in astronomy). These quantities are sometimes called intensity, but this usage leads to confusion with radiant intensity, which has different units.
All of these quantities characterize the total amount of radiation present, at all frequencies. It is also common to consider each frequency in the spectrum separately. When this is done for radiation incident on a surface, it is called spectral irradiance, and has SI units W/m$^3$, or commonly W/m$^2$/nm.
If a point source radiates light uniformly in all directions through a non-absorptive medium, then the irradiance decreases in proportion to the square of the distance from the object.
