This is not a Linux specific issue, but rather a behavior that manifests when a webpage author decides to specify that fonts should be used to render their website that are not present on your system.
To facilitate this, some will specify font files that the browser should download and use to render their website. In this case, your browser will download the font files they link to and the browser will use these to render the page.
If they don't include them, they will usually specify the font-family that the browser should fall back on in the CSS so that they browser can render the page as close to what they had intended as possible.
Both browsers allow you to disable downloading the fonts and use your system fonts in their place.
To override in Firefox:
Enter about:config
in the address bar. Search for gfx.downloadable_fonts.enabled
and change this flag to false
. This option will be saved to your ~/.mozilla/firefox/prefs.js
file which will then be loaded every time your start your browser.
To override in Chrome:
Launch Chrome from the command line:
google-chrome --disable-remote-fonts