Okay, here it is. The difference between Active and Corresponding memberships depends on location of residence as EnglishChineseT mentioned. Both have to go through the certification process. Otherwise the status is an associate.
http://www.atanet.org/docs/p_bylaws.pdf
a. Active:
1) Any person who (a) is professionally engaged in translating, interpreting, or closely related work, (b) is a citizen or permanent resident of the United States, and (c) has passed a certification examination administered by the Association or has achieved demonstrable professional status as determined by peer evaluation, is eligible for Active membership.
2) Members having Active status at the time provision a.1) went into effect will retain their status as long as their membership is not terminated and they continue to remain a citizen or permanent resident of the United States.
3) Active membership is in the name of the individual only and confers no Corporate or Institutional membership on the individual's company, employer, or institution.
b. Corresponding:
Any person who meets all qualifications for Active membership except U.S. citizenship or permanent residence is eligible for Corresponding membership.