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Any font rendered by the system is going to look different from OS to OS, even if it is a “web safe font”. The same font files on different operating systems may even produce different results!
The answer is to use web fonts, which are hosted online and partially rendered by the browser. Things like Google Web Fonts and Font Awesome are examples. The browser itself if responsible for most of the rendering process, however the subpixel rendering or anti-aliasing differs from OS to OS. For example, Google Chrome and Firefox may look slightly different, but Firefox on Ubuntu, Mac, and Windows will all render the font the same way – meaning that they will look identical in size, thickness, and spacing on all operating systems. Mac for example, won’t use subpixel rendering, but it will line up with other operating systems on the same browser just fine.