In general, Trump does better when respondents don’t actually have to tell another live human being that they plan to vote for Trump.
Which, then, is the more accurate approach for gauging voter sentiment? It may depend on the nature of the contest you’re polling.
In New Hampshire, voters will disappear into a voting booth and select their choice for the nomination. They won’t have to tell another soul if they voted for Donald Trump. In this case, the fact that respondents in an online poll also get nearly perfect anonymity may more closely mirror the actual act of voting.
But in Iowa, or in other caucus states, the selection process will involve discussion and a public airing of one’s preferences. In that case, telling someone live over the phone how you feel may be closer parallel to the caucus process.
All of which is to say that we may have a few different factors in play here: Some people may say they plan to vote for Trump, but, in reality, they haven’t had to deeply consider the question and so they just say the last name they heard on the news. However, some people may be afraid to say they support Trump, but in the privacy of a voting booth would make that preference known with their secret ballot.