Here is a very quick list of the most used words and phrases used when working with typoghraphy. I have grouped them into two groups to easier navigate through the list.
Families, Types & Formats:

Type refers to a single character, and could be any character used including numbers and symbols (“, Kk, 10)
Typefaces are actually font families. This refers to families of the same fonts that differs slightly. An example could be the myriad family which consists of: Myriad, Myriad Std and Myriad Pro
Size & Spacing:
Font is a particular set of characters defined within a typeface. For example to use the example from before where the typeface was Myriad, here a font could be Myriad Pro
Variants is the variant of a particular font, for example the font Myriad Pro has a ton of variants including:
Types of fonts refers the the style of the font ie. Serif or sans-serif:
Sans-Serif is fonts without serifs’ which is easily explained by showing a serif. A serif font is a font where each character varies in size like Times New Roman. It has small handles which makes it easy to read even when the print is small. Sans-serif is then the opposite here the characters has the same thickness throughout the characters, and does not have any handles. An example here could be Arial
Others more sparingly used are script and decorative. Script is used to mimic handwriting and decorative is used for more denotative titles mostly. A well known decorative font is the ones used to mimic old western movies like Rosewood Std. Script is used mostly when signing digital documents, its used to give the feeling of a handwriting. An example could be Brush Script Std
Type 1 or postscript is a type developed by Adobe and is a professional choice of font. Type one is some where identified with the red (a) icon
True Type is developed by Apple and was a reaction on the high license costs of Type 1, True Type can cause problems when it is sent top a printer, it is often identified by the (TT) icon
Open Type is way the most popular and can be seen a bit like the open source of fonts. The source code of these font are more or less open to make changes to a certain set of fonts. Thses fonts also works on all platforms wheter on a mac, windows or linux(O)
Size & Spacing:
Leading is the space used between two lines of text. This can be used top separate headlines from body text or create an easier readable document.
Kerning is the space between individual characters, and is used to space letters or numbers apart. This can be very useful in headlines and other scenarios where it can be hard to read a certain word. These problems mostly occur if you are using very large or very small font sizes
Tracking is the space between a set of words. Usually seen in newspaper columns where each line is exactly the same length. This is also called justification of text
Points is a way of sizing text. 12pt is a standard in most word processors for example
Picas & ems refers to a unit. This would in most cases be 12pt. But it depends on what the default size is, if the default size in a document is set to 18pt then 1em would refer to 18pt, meaning that 2em would be 36pt.SerifBrush