I think you're on the right track here: version implies a bigger difference than variant.
The first Oxford definition of each are similar, but they have some key differences:
Oxford definition of version:
A particular form of something differing in certain respects from an earlier form or other forms of the same type of thing:
Oxford definition of variation:
A form or version of something that differs in some respect from other forms of the same thing or from a standard:
Looking at version, Y is a version of X if it differs from
- an earlier form
- or another form of the same type of thing
On the other hand, Z is a variant on X if it differs from:
- other forms of the same thing
- or a standard
The "earlier form" is the most straightforward difference: variant does not mention "an earlier form".
The second distinction is between another form of the same type of thing vs. the same thing or a standard.
There are some gray areas here as to what the "same thing" is vs. the "same type of thing". If car A and car B are distinct only in their color, you would probably say they are the same car that differs in some respect. However, if car A has a v6 engine and a hatchback, where as car B has a v4 engine and a small trunk but are otherwise the same, you might say car A and car B are the same type of car (the hatchback and sedan versions).
An example of differing from a standard is if there is a specific strain of a very common virus: you would say it was a variant.
Some common usages of each:
Version (examples summarized from the Oxford definition):
- The abridged version of my favorite book
- The latest version of antivirus software
- My version of the story
Version is very commonly used to described "An adaptation of a novel, piece of music, etc., into another medium or style" (Oxford definition), in describing software, or describing two critically different viewpoints on the same topic.
Variant (summarized from the Oxford definition and Merriam-Webster) :
- Gray is a spelling variant of grey.
- A more deadly variant of the disease.
Variant is used to more to describe slight changes, such as a different letter in spelling. It also has the very specific use of strains of diseases.
They kind of mean the same thing, but tend to be used differently
Non-alcoholic is commonly used when referring to beverages[1].
Additional, you can use Alcohol free can be used when referring to a trace amount of alcohol[2]
So which one you're using generally depends on the context.
Best Answer
They mean essentially the same. "Of" is more likely to be used when "break free" is used figuratively to imply freeing something from the influences of something else, while "from" is more likely to be used when physically separating something from something else. But that's not a hard-and-fast rule.