The reason for the discrepancy apparently lies in the fact that different surveys poll different segments of the electorate. Claudia Deane of the Pew Research Center has written a very helpful article which clarifies a lot about how these polls are conducted and why different polls come up with such disparate results. She writes:
There are a number of possible reasons for polls arriving at different estimates – from the mode used to collect data to how people are selected for a survey – but here we’ll tackle one of the most basic: Did the poll include or exclude the 45% of adult Americans who didn’t cast a vote last November?So, President Trump fares better among those who are actually likely to vote than among the population at large. In other words, many of those who don't like the president's performance thus far didn't vote in November and thus have only themselves to blame.
Typically, polls in the U.S. are designed to represent one of three populations. The broadest is the general population of all adults (GP). Surveys based only on adults who are registered to vote (RV) apply a narrower lens on the public. Narrower still is the filter applied with surveys that interview only registered voters who are deemed likely to vote (LV). Many pollsters might conduct surveys of all three, depending on where they find themselves in the election cycle.
In non-election years like this one, most pollsters survey all adults, but not all follow this convention. A number of pollsters continue to do surveys of registered or even likely voters. Why does this matter for Trump’s approval ratings? It’s about demographics. Voters as a group skew older and whiter than the general public. And older Americans, as well as white Americans, tilt more Republican than other groups. So, voter-only polls tend to get somewhat more favorable views of a Republican president or candidate and less favorable views of Democrats. This pattern was evident during Barack Obama’s presidency, with his overall ratings tending to be somewhat higher among the general public than among registered or likely voters.
A look at some of the presidential approval numbers released this month shows a pattern consistent with these demographic differences. LV polls – those surveys based only on the views of “likely voters” – are generally reporting higher levels of support for Trump than general population polls. There is a more muted but still significant difference in an RV-GP comparison: Pew Research Center’s general population poll conducted Feb. 7-12 recorded Trump’s presidential approval rating at 39%. Among registered voters in that survey, his rating was 42%.
In the U.S., roughly six-in-ten adults are registered to vote. This means that RV polls, by design, exclude nearly 40% of adults living in the U.S. and LV polls ... exclude even more, as they aim to include only those registered voters who actually cast, or will cast, a ballot. The voting rate among adults ages 18 and older was 55% in the 2016 presidential election and 33% in the most recent midterm election.The question is, though, what do the opinions of those who don't care enough to vote matter? If people are too apathetic to bestir themselves to the voting booth then surely they're too apathetic to inform themselves on what's actually going on, so why should anyone care about what they think?
If a pollster is currently conducting an LV poll with 2018 (a midterm election year) in mind, then recent midterm voting behavior suggests that their results might be excluding the views of a majority of adults in the U.S.
Non-voters skew more Democratic which means that if all non-voters had voted in November Hillary Clinton would probably be president today. Unfortunately for those who lament the fact of a Trump presidency, a sizable percentage of Democrats just don't care. Of course, the same could be said of the majority of Republicans, but in their case enough did care to elect not only the president, but also majorities in both houses of Congress and, since 2008, a substantial number of governorships and state legislative seats.
The picture looks even bleaker for Democrats in the 2018 midterm elections unless they up their game and get their people to care enough about who runs the country to go to the polls on election day.