OpenType and TrueType Fonts Are Closer Than They Look
The difference between OpenType and TrueType is less useful as a purchasing rule than the file extensions suggest. Both formats are widely supported, and an OpenType font can even contain TrueType-style outlines.
What matters is the particular font: its outlines, character set, OpenType features, hinting, and licence.
The outline format is one real difference
Classic TrueType fonts use quadratic Bézier curves for glyph outlines. OpenType is a broader container format and can use either TrueType outlines or PostScript-style CFF outlines, which use cubic Bézier curves.
That distinction affects how the font is built, but it does not mean one format is automatically sharper or smaller. The quality of the typeface and its hinting matter more than the label alone.
OpenType can carry richer typography
OpenType supports tables for typographic features such as ligatures, small caps, alternate glyphs, and language-specific substitutions. It can also contain large character sets for multiple languages and writing systems.
TrueType is also table-based, and modern TrueType-flavoured OpenType fonts can include those same OpenType layout features. This is why treating .ttf as “basic” and .otf as “advanced” is too simple.
Which one should you use?
Windows and macOS support both formats, as do common design applications. For web use, I would normally serve WOFF2 rather than a raw .ttf or .otf file because WOFF2 is packaged and compressed for the web.
If you are choosing between two desktop font downloads, check which one contains the glyphs and features you need. A good TrueType font is a better choice than an OpenType file that is missing the right language support—and the extension cannot answer that for you.