Meaning of units in ELISA based tests?
The ELISA kits are calibrated to meet the requirements of
  internationally certified laboratories such as Center for Biologics
  Evaluation and Research (CBER) associated with FDA. In most cases, the
  presence and specific concentration of an antigen is the target for
  the measurements. Such measurements take place through the absorbance
  measurement. According to the Beer-Lambert law, concentration of a
  compound in a solution is proportional to the quantity of light
  absorbed at its specific wavelength and at a constant optical
  path-length. Following absorbance measurement, a simple calculation
  leads to the concentration of the analyte via equation below: 
  
  A = εlc 
  
  where A is absorbance of the solution at the particular wavelength, ε
  is the molar absorptivity, l is the path length or deepness of the
  solution (which for common spectrophotometers is 1 cm or less if a
  well plate reader is employed), and c is the concentration of the
  substrate in the reaction solution (M or mol/dm3). Majority
  of ELISA microplate readers correspond to this method for the
  calculation of the analyte concentration. Introducing standard
  solutions with known analyte concentrations can be the basis of such
  calculations for the instrument. Measurement unit are typically
  expressed in gram per liter (g/l), mol per liter (mol/l) and copies
  per milliliter (copies/ml) for nucleotides, plaque forming units per
  milliliter (pfu/ml) for infectious viruses, colony forming units per
  milliliter (cfu/ml) for cells and phages, as well as unit per
  milliliter (u/ml) for specific enzymes. These measurement units can be
  also reported over time (i.e. ng/ml/h). Relative units (RU/ml) or
  equivalent units (Eq/ml) are normally used if no international
  standard references exist for the conversion.


Source: Enzyme-linked Immunosorbent Assay (ELISA): From A to Z (SpringerBriefs in Applied Sciences and Technology) by Samira Hosseini, Patricia Vázquez-Villegas, et al. | Dec 31, 2017; ISBN-13: 978-9811067655; ISBN-10: 9811067651. Page 65.

Contrary, Units Per Millilitre (U/mL) are normally used when there are international standard references, agreed upon by scientists and doctors.

Please find the following information on Arbitrary Units (AU):


  The WHO Expert Committee on Biological Standardization (ECBS) is the
  scientific body that establishes WHO biological reference standards
  which serve to define an internationally agreed unit to allow
  comparison of biological measurements worldwide. WHO International
  Standards (IS) for biological substances are recognized as the highest
  order of reference materials for biological substances and they are
  assigned potencies in International Units (IU). International
  Standards are used to quantify the amount of biological activity
  present in a sample in terms of the IU, allowing comparisons between
  assays from different laboratories.  Calibration of assays using
  System of Units (SI)units is not appropriate given the variability of
  the specific activity of a biological material. Use of an arbitrary
  unit makes it possible to better define parameters such as the
  analytical sensitivity of tests or clinical parameters such as
  protective levels of antibody.


Usually, arbitrary units are defined within a particular study. For example:


  A human serum pool positive for anti-dsDNA IgG antibodies (DNAPo) was
  prepared by mixing equal parts of serum from 10 patients with SLE who
  had a positive CLIFT test ≥ 1:640. The DNAPo was arbitrarily designed
  as having 100 arbitrary antibody units (AU) per ml. Artificial serum
  standards containing different AU/ml were prepared by diluting the
  DNAPo with phosphate-buffered saline (PBS) containing 0.1% Tween 20
  (PBS-T). A human serum pool negative for anti-dsDNA IgG antibodies
  (DNANe) was prepared by mixing equal parts of serum from 10 healthy
  persons who had a negative CLIFT test and no clinical evidence of SLE.
  The DNAPo and DNANe pools were used as positive and negative controls
  in the ELISA and CLIFT reactions.


Thus, the U/mL figures are comparable, while RU/ml or AU/ml are not.