Regarding glyphs and characters:

A character is an encoded semantic entity, e.g. 'Latin uppercase A' encoded in Unicode as U+0041.

A glyph is a particular representation of a character, multiple characters (ligature), or even part of a character. A font is a collection of glyphs, some or all of which may be directly mapped to characters. It is possible for a font to include 'unencoded glyphs', i.e. glyphs that are not directly mapped to characters, but only indirectly mapped via glyph lookups. So, for example, a regular uppercase A, a smallcap A, and a swash A are all glyph representations of the character 'Latin uppercase A', but only one of them will be directly mapped to the character codepoint U+0041. The others may be called 'expert glyphs', but the more usual term is 'variant glyphs'.

Well said, John. No argument here. I was just trying to keep things basic.

glyph: A character's form or shape in a font.
expert glyphs: This may not be correct usage. The usual term would be expert characters. It means characters intended for use in more refined typesetting, such as small caps and ligatures (see below).
hanging figures: Number characters which sometimes hang below the baseline. Also called old style, ranging, or lowercase figures.
lining figures: number characters which are all the same height
monospaced: All the same width (as on a typewriter). Monospaced figures are designed to line up neatly in tables or colums of figures.
proportional: Varying widths. Proportional figures are designed to look better in headlines and text.
(Usually, figures are monospaced, whether hanging or not. de Groot is saying he also provides proportional sets of both styles.)
fraction figures: A set of small number characters, both superior and inferior, for creating arbitrary fractions (e.g. 13/457). A special fraction bar character is used with these. An example of something which would be part of an expert character set.
f-ligature: A ligature is a pair of characters combined into one character, usually to solve awkward spacing problems, but sometimes decorative. An f-ligature would combine f with some other character (fi, fl, ff, ffi, ffl, are typical). f-ligatures are the most common kind of ligatures. The top of the f in many typefaces extends far enough to the right that it can cause problems when setting next to certain other characters (mainly i and l). Ligatures are designed to solve this type of problem.