If I understand your question and the term "soft EHL" (soft solid materials?) correctly, there will be some differences.

In traditional EHL, solids are made from hard materials. The contact surface is therefore relatively low, the contact pressure is high (1 GPa or more) and the film thickness is very thin (100-200 nm).

The situation is significantly different in soft EHL: large-size contacts, medium pressure, thicker film thickness.

This will necessarily have consequences on how to solve the problem numerically even if the fundamental equations are the same or almost the same. Reasons among others: the effect of pressure on lubricant viscosity, the extension of the deformed solids zone will be very different, which will very likely require a re-examination of the adimensionalisation and numerical resolution strategies,

If I understand your question and the term "soft EHL" (soft solid materials?) correctly, there will be some differences.

In traditional EHL, solids are made from hard materials. The contact surface is therefore relatively low, the contact pressure is high (1 GPa or more) and the film thickness is very thin (100-200 nm).

The situation is significantly different in soft EHL: large-size contacts, medium pressure, thicker film thickness.

This will necessarily have consequences on how to solve the problem numerically even if the fundamental equations are the same or almost the same. Reasons among others: the effect of pressure on lubricant viscosity, the extension of the deformed solids zone will be very different, which will very likely require a re-examination of the adimensionalisation and numerical resolution strategies,

I agree with Professor Philippe Vergne 's answer. Besides, I want to add one item: Soft EHL happens with big elastic deformation, which might be much larger than the size of the body itself.

An alternative way to look at soft versus hard is from the viewpoint of the dimensionless parameters. Soft versus hard is essentially captured in the so-called lambda parameter in the Reynolds equation when scaled on e.g. the Hertzian contact parameters. This parameter can be seen as the ratio of the viscous forces (in the inlet region) over the elastic forces. More detailed explanation can be found in the paper

Similarity theory of lubricated Hertzian contacts

J. H. Snoeijer J. Eggers and C. H. Venner

PHYSICS OF FLUIDS 25, 101705 (2013)

in particular see equation (9)