I don't know if Factorio actually uses it, but there's a system called symantic versioning that is often used and very useful in software, and even when it's not formally used, the fundamental principles are loosely adhered to. Simply, symver says you have 3 basic numbers in your versioning, XX.YY.ZZ (ie 1.2.73) that are defined as such, with possible implications for a game like factorio:
XX - Backward Incompatible Features. major changes _that break previous compatibility_. Changes like this would likely see mods break completely, saves may not carry over or require big conversions that may break some aspects of the save.
YY - New, Backward Compatible Features. minor changes or feature additions that do not break any backward compatibility. Mods would likely work, but mod makers may want to add bits to their mods to tie into new features. Save files would likely be safe.
ZZ - Minor bug fixes. Generally no new features, mods & saves would likely...