What is the difference in mosM and mOsm units, if there is any at all?

Question

I'm reading Agre's paper on aquaporins [1] and he uses a unit called "mosM" throughout the paper, for example:

… ocytes were transferred from 200 mosM to 70 mosM modified Barth's buffer.

I just want to understand what this unit means, is it the same as mOsm? I know this might be an very stupid question but hey, I'm only a undergrad.

Reference

1. Preston, G. M.; Carroll, T. P.; Guggino, W. B.; Agre, P. Appearance of Water Channels in Xenopus Oocytes Expressing Red Cell CHIP28 Protein. Science 1992, 256 (5055), 385–387. DOI: 10.1126/science.256.5055.385.

Answer 1

I think the clinical chemistry notation has not been standardized but certainly it has been inspired by chemists.

The capital M in mosM emphasizes that it is milliosMolar. Chemists use capital M to denote molarity.

On the other hand, mosm indicates milliosmolal. Chemists use small m to symbolize molality.

This notation is not universal.

From this slightly dated article on Osmolality, which is behind pay-wall Osmolality, Harry F. Weisberg Laboratory Medicine, Volume 12, Issue 2, 1 February 1981, Pages 81–85.

Terminology and Units

In 1934, Gamble, et al.,¹¹ introduced the term ”osmillimole” which has been successively transformed into mosM (milliosmolar), mosm (milliosmolal), the noncommittal mOsm, and the present-day mosmol (milliosmole). Raoult’s law states that the lowering of the vapor pressure (one of the four ”colligative” properties of dilute solutions) is proportional to the mole-fraction (more easily calculated from molality) of solute present in the mixture.

Answer 2

Judging from the following table consisting of compiled notations presented in offline edition of The ACS Style Guide and AMA manual of style, section 13.12 Units of Measure:

$$ \begin{array}{ll} \hline \text{Unit of measure} & \text{Symbol} & \text{Ref.} \\ \hline \text{osmolar} & \text{osm (also osM, Osm)} & \text{[1, p. 191]} \\ \text{osmole} & \text{osm} & \text{[2, p. 635]} \\ \text{microosmole} & \text{µOsm} & \text{[2, p. 634]} \\ \text{milliosmole} & \text{mOsm} & \text{[2, p. 634]} \\ \hline \end{array} $$

symbols $\pu{Osm}$ and $\pu{osm}$ refer to the amount-of-substance of an osmotically active entity, and symbol $\pu{osM}$ refers to osmolar concentration suggesting the following relation:

$$\pu{1 osm L^-1} = \pu{1 Osm L^-1} = \pu{1 osM}$$

The letter “o” in $\pu{Osm}$ appears to be capitalized for the sake of better readability when used in conjunction with metric prefixes, and the letter “m” in in $\pu{osM}$ is likely capitalized to resemble analogy with the unit symbol for molarity (small capital letter “m”: ᴍ).

References

1. The ACS Style Guide: Effective Communication of Scientific Information, 3rd ed.; Coghill, A. M., Garson, L. R., Eds.; American Chemical Society; Oxford University Press: Washington, DC; Oxford; New York, 2006. ISBN 978-0-8412-3999-9.
2. AMA Manual of Style: A Guide for Authors and Editors, 11th ed.; American Medical Association, Ed.; Oxford University Press: New York, 2020. ISBN 978-0-19-024656-3.