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.
The Type1 font standard was devised by Adobe, and Type1 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 Type1 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 Type1 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.
True type fonts were developed by Apple. They made the format available to Microsoft, and succesfully 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.
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 Type1 and TrueType fonts, both have a lot in common. Both are scalable outline fonts. Type1 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 ( Type1 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 Type1 fonts are in availability and application support. The widespread availability of TrueType fonts for Windows has resolted 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 Type1 fonts but do not have the same level of support for TrueType. Moreover, most major font foundries still ship most of their fonts in Type1 format. For example, Adobe ship 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 ).
Metafont was developed by Donald E Knuth as part of the TeX typesetting system. Metafont is a graphics programming language ( like postscript ) that has applications wider than just fonts. Metafonts exhibit some very desirable qualities. One of the important features is that metafonts can scale very gracefully. The metafont Computer Modern has different shape at 20 point and 10 point. The shape changes with size, because it is desirable for a smaller font to be proportionately wider than a larger font ( this makes the larger fonts more elegant and the smaller font more readable ).
Metafonts typically have a mf extension. They are rendered to device dependent bitmap fonts. The rendering is slow, so they are of excellent quality, but are not well suited to WYSIWYG publishing.
Typically typically come in groups of a few variants. For example, most fonts come with a bold, italic, and bold-italic variant. Some fonts may also have small caps, and demibold variants. A group of fonts consisting of a font and its variants is called a family of typefaces. For example, the Garamond family consists of Garamond, Garamond-italic, Garamond-bold, Garamond bold-italic, Garamond demi-bold, and Garamond demi-bold-italic. The Adobe expert Garamond font also makes available Garamond small caps, and Garamond titling capitals.