First, those are two different fonts. "Monospace" is a font-family (like Serif, Sans-Serif, etc.), not a specific font. Monospace means that each character has the same width as all the others, and is commonly used for code so that it lines up with the code above and below for readability. (It's easiest to see that those are different fonts by comparing the
Second, both Windows and Ubuntu have what is known as font smoothing. Most fonts are vector-based, which means they're defined as curves and lines - this is great for scaling them up to any size, but bad for actually rendering them to pixel-based screens. There are a series of techniques which are used to improve font rendering, and depending on which ones you use, the fonts can look slightly different.
If you're unhappy with how Windows is rendering fonts, you'll want to turn on ClearType (it looks like it's already on) and then run the ClearType configuration tool:
- Open the Control Panel
- Search for
- Select Adjust ClearType text
- Make sure ClearType is enabled, and then follow the prompts by clicking the version of the text that looks best on your screen.