What is the difference between TrueType fonts and Type-1 fonts?
A very key difference is that PostScript (and PostScript flavoured OpenType) supports cubic Bézier curves, where each arc of each glyph is described by four control points. TrueType (and tt flavored OpenType) uses quadratic curves, with each arc having only three control points. This offers less control over the shape of the curve.
Another key difference is the way they perform hinting. Since TrueType was originally targeted to low resolution screen rendering, its hinting system works by adjusting the curves to fit nicely on pixel lattice points, using a fairly elaborate bytecode mechanism. PostScript fonts were intended for higher resolution paper prints, and used guidelines to snap curves to right angles at appropriate places.