Confusion about changing meaning of arguments and options, is there an official standard definition?

I came across a confusing variation in the understanding what options and arguments are with regard to the syntax of commands. For instance, I encountered definitions like: - command -a -b -c d e f some differ between -a -b -c, call them options or switches and d e f by calling them arguments. - command -a -b -c d e f some, for instance a bash manual, call all -a -b -c d e f arguments and explains, that all of them are accessible from a script by $1 $2 $3 $4 $5 $6 respectively. - command -a b=c some call -a an option, b an argument and c the value, but others mix them like in the first two points, in one variety calling all -a b c arguments. Those three versions are only examples for a plethora of different calling varieties, I do not even know how to list them all, but I noticed that for sure there is no fixed naming convention. Or at least, there is no standardised naming convention I know about, because I came across different random sources, but even among official Linux and GNU affiliated sites or manuals I could met this inconsistency. Is there a unquestionable official naming scheme I can refer to?