A font is a complete character set of a single size and style of a particular typeface, or family of fonts, very much like an individual with the last name Palatino would belong to the Palatino family; 12 point Palatino Bold is an individual font from the Palatino typeface family. Some fonts and their typefaces have been in use for hundreds of years.
Caslon was invented by William Caslon I (1692-1766). Like all the typefaces it's seen various updates as printing technology has advanced. One of Caslon's typefaces was actually used on the Declaration of Independence. His foundry continued to operate for over 200 years. The font is balanced and easy on the eye, with the capital "A" having a subtle bit of a beak. There's also a somewhat drooping terminal on the lowercase "c."
Garamond is quite an old typeface named after Claude Garamond (1480-1561), a Parisian publisher who became famous when his Greek typefaces were requested for a royally commissioned book series by Robert Estienne. Garamond is a somewhat more stately typeface than Caslon, with clean upper case letters and no ascenders (when lower case letters like "d" or "l" are taller than the uppercase letters).
The graceful and very readable Goudy Old Style was created by Frederic W. Goudy in 1915 for the American Type Founders. The arch on the lowercase "n" has a distinct downward slope. The lowercase "d" and "l" have ascenders, and the tail on the lower case "e" is especially pointed. Goudy Old Style is the typeface used in Harper's Magazine.
Baskerville was designed in 1757 by John Baskerville (1706-1775) of Birmingham England. It's designed to be an improvement on Caslon typefaces. It's quite readable, and its most notably different feature from the other fonts is that the loop on the lowercase "g" is open. The eye -- the white space -- in the "e" is also a bit higher up in the letter than in many other fonts.