A website can work out which fonts you have without asking. It measures a piece of text in a candidate font and compares the size with a fallback font. If the size differs, that font is installed.
Why fonts are distinctive
Your operating system sets the base list of fonts. Office suites, design tools and language packs add more, so the exact set can say a lot about a device. Someone with professional design software often stands out.
Measurements also matter
Even with the same fonts, text can measure slightly differently between systems because of rendering and font versions. Emoji are a good example: their size and style change with the operating system version.
How to check yours
Run the PrintLeaks test and open the Fonts and locale tab to see what your browser exposes.