The International Standards Organization (ISO) Standard 12757 includes a classification system for ballpoint pen refills. That standard identifies a variety of standard refills, defines the critical dimensions, and in some cases, establishes a link to a specific manufacturer. For example, a C1 refill is generically called a 'Cross style' refill because it covers refills that fit Cross pens., while a 'Parker style' refill is ISO G2.
The problem with international standards is that there are no standards police to make sure that everyone follows the rules. So even the vaunted Cross refill is subject to variations, including by Cross itself. For example, the ISO standards says that a C1 refill is 117.5mm long, but the refills made by Cross are 115.9mm long, and S. T. DuPont make a C1 refill that is 112.4mm long. My experience is that a C1 refill branded (and presumably made) by Cross or Schmidt will usually fit kit pens that are sold as 'Cross Style'. That small difference in length gets taken care of when you adjust the placement of the transmission to achieve the desired exposure of the nib.
Likewise, a 'Parker style' ISO G2 has a length of 98.2mm, but in practice, the length varies from 94 to 99mm, with the difference causing variations in how much nib is exposed when it is in the writing position.
In addition to specifying length, the ISO standard also specified diameter. The diameter over the main portion of the body is usually not critical, but there have been numerous posts on this board about variations in the diameter of the nib, and in particular, concerns that the nib on some refills appears to be larger than the opening in the nib cone that it is supposed to fit through. However, this may also reflect variations in kit manufacturing rather than variations in the refills themselves, and known fix is to use a drill bit to ream out an undersized nib cone.
In my experience, 'Cross style' and 'Parker style' refills from either the named manufacturer, or one of the very reputable aftermarket manufacturers like Schmidt or Monteverde will generally fit pens sold in those generic classifications. The same cannot be said for refills from no-name suppliers in Asia.