It’s easy to forget how hard it is to standardise a large populous given everything these days can be shared at near-to-light-speed but even today you have regional slang. Terms that might be common in the north of a country but alien to southerners.
So I find it entirely believable that there were multiple “standards” for Roman numerals that spanned different regions and periods of time.
The reality is far more likely that the notations IIII and IV were equivalent, to any numerate person of the era; and if asked about what the difference is their response would likely be the same as a modern person being asked about the two glyphs for "a" and "g" in many English alphabet typefaces (or even the various open and closed glyphs that Indian numeral "4" can have). They are so used to the forms that they don't even register a difference that is glaring to outsiders, let alone consider one to be "wrong" and the other "right".
That indeed seems to be the case. Apparently it largely standardized at some point in the Middle Ages as usage was decreasing. Although I can't find a reference, it's logical to assume given the timeframe and place that the Church probably had something to do with the standardization whether formally or otherwise.
