What is the standard practice?
vim to start the command or its common alias
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There is probably no way of knowing the answer to your question. I would hypothesize that there is an age bias, with older users using "vi" and younger users using "vim" or "gvim".
Some distributions include "vi" but not "vim" in the default installation. Occasional users of those systems are probably not going to install "vim".
Embedded Linux filesystems based on Busybox and similar have only a stripped down version of "vi" with no "vim" at all, and no space for it.
In any event, if you are scripting, you would be best not to make any assumptions and retain the distinction between "vi" and "vim".
If you are setting up default aliases for your users I would advise against automatically aliasing "vi" to "vim". Some users might want to retain the distinction. Others should add their own aliases, or uncomment a commented alias that you provide.
If you are teaching, then you need to explain the differences between "vi" and "vim" derivatives such as "gvim" and you need to explain the common aliases.