The debate among blacks comes at a time when other minority groups are also struggling toward redefinition. In recent months, Jews here and in Israel have been torn over the question ''who is a Jew?'' Hispanic Americans have grappled with the use of Latino and Hispanic. And Asian-Americans, seeking recognition of their many nationalities, have successfully lobbied the Census Bureau to delineate Asian groups in the 1990 census, even listing Samoans and Guamanians.

The push for a change from ''black'' to ''African-American'' came too late to become a category in the 1990 census, said Nampeo McKenney, director of the agency's special populations division. The form will say ''Black or Negro'' in the section on race. But in light of growing pressure, the agency is adding special instructions telling those filling out the forms that ''Black or Negro includes African-Americans.'' The term African-American cannot be used officially until the agency tests it in a process that takes several years, she said. Turning Point Is Seen

Still, the push by Mr. Jackson is seen by black historians as an important step. ''This is a significant psychological and cultural turning point,'' said Dr. Walter Allen, a professor of sociology at the University of Michigan who is black. ''This makes explicit what was implicit. First we had to convince everyone to come into the fold as black. Now we are clarifying what that means.''

Dr. Ramona Edelin, president of the National Urban Coalition, said: ''There were bitter battles when we went from 'Negro' to 'black.' We don't want that this time.'' Dr. Edelin said that when she brought up the idea for adopting the term African-American at a meeting of 75 black groups convened by Mr. Jackson late last month, there was ''overwhelming consensus'' favoring the change. The meeting attracted scores of people from fraternities, sororities and civic and social groups.

Several school districts, including Atlanta and Chicago, have adopted the term in their curriculums and encourage teachers to use it. ''We just feel it's a more accurate term,'' said Dr. Alice Jurica, director of social studies for the Chicago public schools.

Two of the largest black-oriented radio stations in New York City, WWRL and WLIB, have been using the term. Now more listeners who call in refer to themselves as African-Americans, although once they get going they often slip back to using black, said David Lampel, WLIB program director. ''Often they will use black and African-American in the same phone call,'' he said. Changes in the Press

The heightened awareness has brought a bit of confusion. The station recently broadcast a report that referred to a woman with a dark complexion and a Hispanic surname. ''Everybody in the newsroom was struggling with what to call her,'' Mr. Lampel said. ''They decided on African-Latino.''