You will find that the developers themselves are not using short variable names. Whilst developing, they are using meaningful and detailed variable names.
Then, in the build/release process, the code they've written is ran through a minifier/obfuscator with the intention of minimizing the size of the file, as a best practise to speed up a website. This is an optional step if you care that much about performance. Most small websites don't do this.
You, as a developer, should not care about the minification/ obfuscation process; write your code so that it is readable, meaningful, well documented and well structured. Then if you care so much about performance (optional, don't forget!), introduce a minifier/ obfuscator into your release process to minize the code (remove white space, new lines, comments etc) and to obfuscate it (e.g. shorten variable names). A good article which explains obfuscation vs minification can be found here.
Additionally, Desktop FireFox will not truncate variable names period. The truncation of variable names is there to speed up the page download. By the time FireFox gets the file, it has already been downloaded therefore there is no need to do so. Your friend may run a plugin which is doing this; in which case, tell him to uninstall it, because it's useless.
For completion, some (mobile) browsers have the option to use middle-man servers, which intercept the responses of resources you requested, and compress them for you (which could include the minification of JavaScript files). Note that the compression is done on the server (i.e. before you have downloaded the page), hence the potential benefit of downloading a smaller file, rather than in the browser once you have already downloaded the file (as suggested in the question). Such mobile browsers include Opera Mini, and newer versions of Google Chrome (on iOS at least; not sure about Android). For more info, see here.