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The luminosity distance $$d_l=(1+z)r(z)\ ,$$ where $r(z)$ is given by $$r(z)=cH^{-1}_0\int_{0}^{z}\frac{dz'}{E(z')}\ .$$

When I use the SNe dataset "Pantheon", I find there are two redshifts: $z_{cmb}$ and $z_{hel}$.

In some files, the luminosity distance is also written as $d_l=(1+z_{hel})r(z_{cmb})$ (For example 1912.11879 and 2202.12214). This paper 1312.0184 said it is “Since the time dilation part of the observed luminosity distance depends on the total redshift zhel (special relativistic plus cosmological)”.

Why is the luminosity distance related to both heliocentric redshift and CMB restframe redshift? In which situations can it be used?

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I find some clues at terms "Distance measures (cosmology)":

the redshift that would pertain in that case should be used but $d_{A}$ should be corrected for the motion of the solar system by a factor between 0.99867 and 1.00133, depending on the direction.

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