<p>What is the difference between TrueType fonts and Type-1 fonts?</p>

Type-1 is the older format, and dates back to the days when Adobe where pioneering DTP with PostScript and vector fonts. At the time Type 1 and Type 3 were the only formats understood by PostScript printers, and only Type 1 could include hints needed to make fonts look good, and the format was a trade secret. This way Adobe relegated other font foundries to non-hinted fonts using Type 3 format.
TrueType was invented by Microsoft as a way (a) to break Adobe's monopoly on hinted font formats, (b) to avoid using a format associated with the Macintosh and PostScript on Windows. Internally TrueType used quadratic curves rather than cubic beziers, thus making them faster to render on the screen and on the cheaper non-PostScript-capable printeres used on Windows sytems. TrueType also has better support for Unicode and other things invented since the creation of Type 1. Modern Macs support TrueType as well.
The new format OpenType combines TrueType and Type 1 (the vector data is permitted to be in quadratic or cubic form, so you can directly convert either of the old formats to the OpenType). OpenType also has support for fancy automatic ligatures and glyph substitution, which is nice in English text and vital for text using Arabic or Indian scripts.