INDEPENDENT SAMPLES (covered in Chapter 14 of the book), where a participant in one group (Obama voters, say) cannot be in the other group (McCain voters).
CORRELATED GROUPS (covered in Chapter 15), where the same (or matched) person(s) can serve in both groups. For example, the same participant could be asked to complete math problems both during a period where loud hard-rock music is played and during a period where quiet, soothing music is played. Or, if you were comparing men and women on some attitude measure and your participants were heterosexual married couples, that would be considered a correlated design.
Because the formula for an independent-samples t-test is somewhat difficult to glean from the textbook (you could start at Equation 14.6 and then fill in the denominator with help from Equation 14.2b), here's a simplified graphic I found from the web (original source):
(NOTE: I have edited this page to reflect changes I have made in referring students to different graphics.)
