I agree “universally” may be an exageration. Perhaps easily recognised by Fortran users.
My key point is to read the IEEE754 documentation, which is based on storage size.
It describes a precision that is derived from storage size, not a storage size derived from precision, which is Fortran’s kind approach.
The main source of confusion with early FORTRAN real and double precision was because of the many different hardware storage sizes, which were mostly being rationalised by the 80’s. The IEEE754 standard eliminated most of this, but legacy use of REAL and DOUBLE PRECISION were the problems.
Fortran 90 introduced precision, which to me was back-to-front, as with IEEE754, storage size defines precision. Fortran’s approach is precision defining kind, while storage size does not exist !
Unfortunately there is not much discussion of what precision is or the relationship between precision, round-off and computational accuracy. The required precision varies greatly between different computation approaches. In my finite element analysis for plate bending that uses first and second derivatives, this requires a greater precision than for solid modelling that uses only the first derivative. After a while we get to understand the significance of precision, but in my experience this was not sufficiently taught.