What is the difference between diachronic linguistics and synchronic linguistics?

The defining difference between diachronic and synchronic linguistics study has to do with time. First of all, all linguistic study prior to Saussure was diachronic. The word diachronic does a pretty good job of describing itself. Dia- is a Greek prefix used on loanwords that means "through, between, across, by, of, akin to." The root word chronic entered English as a loanword from the Latin, which was taken from the Greek chronus, meaning time. So diachronic linguistics is the study of language across, through or between time(s).

To put it simply, it is historical language. An example of diachronic linguistics would be the study of how Chaucer's Middle English became Shakespeare's English and then contemporary English. Another is how Old and Middle English managed to separate from German. A contemporary example is the work linguist William Labov has done on tracing the usage and variations of the word for the Philadelphia sandwich called a Hoagie, the linguistic variations of which he has traced through time and changes all the way to the California Submarine sandwich.

On the other hand, synchronic linguistics studies language in a fixed time period without reference to any other time period, either past or future. The concern of synchronic linguistics is to get beneath the variations of words, or content, called parole (e.g., topic) and find the intrinsic relationships of words to other words, the langue of language.

Again, the word synchronic gives clues to its meaning. It's derived from Late Latin and is defined as "occurring at the same time; coinciding in time; contemporaneous; simultaneous; going on at the same rate and exactly together; recurring together." The suffix -ic is a Middle English affix from Latin and is defined as "an adjective-forming suffix with the particular sense 'having some characteristics of'." So synchronic linguistics studies language's characteristics that are carried on simultaneously with and coinciding in time with other characteristics of language without reference to language history.

For example, sociolinguistics may study the occurrence of negative prestige wherein social class tied to the present time affects the absorption of vocabulary and pronunciation of a class lower than the speaker's own social class, which stands in contrast to the norm of absorbing the language traits of a class higher than the speaker's class. Another example is how a creole language develops a complex and unified grammar within one generation of speakers.