It seemed like it would be pretty easy to check this--surely some survey would have asked a question about discrimination and randomly switched between the terms. But despite a good deal of searching, I couldn't find anything. Then I turned to questions that were identical or almost identical except for the terms. There have been a number of the basic form "Would you say there is a great deal of discrimination, some discrimination, only a little discrimination, or none at all against...blacks/African Americans?" The results, with the responses scored as 4, 3, 2, 1, so higher numbers indicate more perceived discrimination.
The black dots represent questions that asked about "blacks," red "African Americans," and green "blacks or African Americans." Questions that included both terms got the highest perceived discrimination; questions that asked about "blacks" may have gotten higher perceived discrimination than those that asked about "African Americans," but it's not clear. Overall, it seems like asking about "blacks" rather than "African Americans" may make some difference, but not much.
It seems like there's a pattern over time: a rise in perceived discbetween the 1970s and about 2000, and a decline since about 2000. But to complicate things, there were also some differences in the response categories, as shown in this figure:
Considering these data, and my previous posts on the general topic (see here for a list), I think there are two distinct trends. First, "racial resentment"--that is, the belief that blacks are actually advantaged--is declining and continues to decline. Second, that the belief that blacks are discriminated against rose from the 1970s until around 2000, but has declined since then. My original suggestion that "racial complacency" is rising seems pretty accurate.