At the most basic level, the difference between these two outline formats is a matter of mathematics (cubic vs. quadratic Bézier curves). But a font’s existence as one kind of outline or another can affect its file format, and not all web browsers support all file formats. Buckle up, the next few paragraphs are going to be turbulent.
No single font file format works in all web browsers (yet), so Typekit serves the most appropriate format to each browser: the emerging W3C standard WOFF (Web Open Font Format) wherever possible, Embedded OpenType (EOT) to Internet Explorer (it’s the only format IE8 and earlier will accept), and either raw OpenType (OTF) or raw TrueType (TTF) everywhere else. Type rendering: font outlines and file formats
The above quote is pulled out of context and makes the series of articles seem more abstruse than it is. Anybody interested in why fonts appear different on different browsers and O/S would love this series of articles.