Many customers who frequent Wendy's are still struggling despite stronger economic growth and low unemployment, according to the CEO of the company, the nation's third-largest fast food burger chain.

Asked about the health of the American consumer from his point of view, Wendy's Chief Executive Officer Todd Penegor told CNBC on Wednesday that "It's still be a bit challenging … [because] about 40 percent of our consumers are $45,000 and under from an income bracket. And they're not participating in the real wage growth to the extent of the rest of the consumer base."

Penegor's assessment stands in stark contrast to what Target CEO Brian Cornell told CNBC last month. Cornell said Target is "benefiting from a very strong consumer environment," adding it may be "the strongest I've seen in my career." Cornell has spent more than three decades in retail.

Perhaps the higher, $64,000 per year, median household income for Target shoppers compared with Wendy's customers can explain the disparity between how the CEOs view trends in consumer spending, which accounts for two-thirds of the U.S. economy.