This section contains both non-usefull (nowadays) and usefull information about how font technology evolved, caracteristics of some of them, and the market dynamics that choosed the most widelly used ones.
The bottom line is: today the de-facto font standard is True Type, Linux has strong support to it with the FreeType library, and sometimes you may need some bitmap fonts for screen, but never for printing.
A bitmap is a matrix of dots. Bitmap fonts are represented in precisely this way -- as matrices of dots. Because of this, they are device dependent -- they are only useful at a particular resolution. A 75 DPI screen bitmap font is still 75 DPI on your 1200 DPI printer.
There are two types of bitmap fonts -- bitmap printer fonts, such as the pk fonts generated by dvips, and bitmap screen fonts, used by X and the console. The bitmap screen fonts typically have a bdf or pcf extension. Bitmap screen fonts are most useful for terminal windows, consoles and text editors, where the lack of scalability and the fact that they are unprintable is not an issue.
TrueType fonts were developed by Apple. They made the format available to Microsoft, and successfully challenged Adobe's grip on the font market. True type fonts store the metric and shape information in a single file (usually one with a ttf extension). Recently, font servers have been developed that make TrueType available to X. And PostScript and ghostscript have supported TrueType fonts for some time. Because of this, TrueType fonts are becoming more popular on linux.
The Type 1 font standard was devised by Adobe, and Type 1 fonts are supported by Adobe's PostScript standard. Because of this, they are also well supported under linux. They are supported by X and ghostscript. Postscript fonts have traditionally been the choice of font for anything on UNIX that involves printing.
Typically, a UNIX Type 1 font is distributed as an afm (adobe font metric) file, and an outline file, which is usually a pfb (printer font binary) or pfa (printer font ascii) file. The outline file contains all the glyphs, while the metric file contains the metrics.
Type 1 fonts for other platforms may be distributed in different formats. For example, PostScript fonts for windows often use a different format (pfm) for the metric file.
These fonts are distributed in a similar manner to Type 1 files -- in groups of afm font metrics, and pfa files. While they are supported by the PostScript standard, they are not supported by X, and hence have limited use.
Type42 fonts are actually just TrueType fonts with headers that enable them to be rendered by a PostScript interpreter. Most applications, such as ghostscript and SAMBA handle these fonts transparently. However, if you have a PostScript printer, it may be necessary to explicitly create Type42 font files.
Despite the historical feuding between the proponents to Type 1 and TrueType fonts, both have a lot in common. Both are scalable outline fonts. Type 1 fonts use cubic as opposed to quadratic curves for the glyphs. This is in theory at least a slight advantage since they include all the curves available to TrueType fonts. In practice, it makes very little difference.
TrueType fonts have the apparent advantage that their support for hinting is better (Type 1 fonts do have hinting functionality, but it is not as extensive as that of TrueType fonts). However, this is only an issue on low resolution devices, such as screens (the improved hinting makes no discernable difference on a 600dpi printer, even at small point sizes.) The other point that makes this apparent advantage somewhat questionable is the fact that well hinted TrueType fonts are rare. This is because software packages that support hinting functionality are out of the budget of most small time designers. Only a few major foundries, such as Monotype make well hinted fonts available.
In conclusion, the main differences between TrueType and Type 1 fonts are in availability and application support. The widespread availability of TrueType fonts for Windows has resulted in webpages designed with the assumption that certain TrueType fonts are available. Also, many users have large numbers of TrueType fonts because they ship with the users Windows applications. However, on Linux, most applications support Type 1 fonts but do not have the same level of support for TrueType. Moreover, most major font foundries still ship most of their fonts in Type 1 format. For example, Adobe ships very few TrueType fonts. My recommendation to users is to use whatever works for your application, and try to avoid converting from one format to another where possible (because the format conversion is not without loss).