yes ppm and molarity are two different things. Molarity is number of moles per liter (mol/l). but, ppm is mass (mg) per liter. both are depends on the molecular weight (g/mol) of a substance. since, molecular weight of IAA (175.18 g/mol) and IBA (203.24 g/mol) are different, the molarity of this substance also different to get  even similar amount  which is o.5 mg/l. and ppm can calculated from molarity through the following formula.

ppm=molarity (M) x molecular weight (g/mol) x 1000

for example,

ppm of IAA,

2.9 x 10-6 M x 175.18 g/mol x 1000 = 0.5 mg/l

where, 2.9 uM = 2.9 x 10-6 M.

ppm of IBA ,

2.5 x 10-6 M x 203.24 g/mol x 1000 = 0.5 mg/l

where, 2.5uM = 2.5 x 10-6 M

A good reason to use mg/L or ppm instead of molarity is when the substance does not have a known or well-defined molecular weight, such as extracts and mixtures. Otherwise, it makes more sense to use molarity when comparing different substances (for potency in a bioassay, for example), since you are comparing them on a molecule-to-molecule basis.

For plant hormones I prefer them to be indicated in ppm in order to compare. with other given recipes.

1. If you know a substance's (1) M.W. (molecular weight), (2) weight and (3) how much water (volume) the substance is going to dissolve in, then you can calculate its concentration in different 'unit'-- either in, µg/mL or µM.

2. g/L is a unit of measurement of mass concentration that shows how many grams of a certain substance are present in one liter of liquid. Molarity (M) is the concentration of a solution expressed as the number of moles of solute per litre of solution. So, two substances with a same g/L can be different in Molarity.

For your second question:

You are right: for MOST people, to publish in papers, they will compare the effect of different concentrations of a treatment for, for example, root formation. For instance, they will compare 0.1, 0.2, 0.3, 0.4 or 0.5 mg/L IAA on root formation, or  0.1, 0.2, 0.3, 0.4 or 0.5 mg/L IBA on root formation. In stead of comparing 0.5 mg/L IAA vs. 0.5 mg/L IBA.

For plant tissue culture, it would be more appropriate to use molarity. With molarity it is possible to compare the effect of different growth regulators on physiological response of the explants/cultures more precisely than mg/l.  

Yes both are different things. Better would b use molarity most appropriate and convenience.

The question has been about ppm or molarity and plant hormones were given as an example.

Maybe the total molarity of a medium, referreing to the ratio od N,P,S,K and Ca makes really the difference between media.

Working with callus on solid medium and perhaps lateron in liquid medium could give already a difference of growth though using the same ppm of a specific plant hormone.

Of course, normally, one does not start with 10 ppm in a solid medium, as the first encounter by the callus to the medium will tell whether it can grow on it. 1 ppm of BA is frequently used though surely as the cells grow and use the hormone only on the surface of the medium, one does not actually know how much of the BA is used until the next transfer. Thus it is not important if you use the term of ppm or molarity. These are only terms for later comparison in articles.