Donald Trump's tirades against Muslims, women, journalists, celebrities and his political opponents have dominated coverage of the US Republican race in recent weeks but they have also masked an important fact about the billionaire property mogul-cum-presidential candidate – he is not actually that right wing.

As was highlighted recently in material distributed by Republican groups in Iowa: at various stages of his career, Trump has said he is pro-choice, that he believes in tax increases, longer waiting periods for firearms and government run health insurance. He even donated money to Hillary Clinton during her previous campaign, leading some to suggest that he is actually more of a Democrat.

Those stances – along with his brash demeanour and New York background – will actually lose him support with the right wing Republicans that are so integral to electing a new US president. Trump may be willing to drum up column inches with racist tirades against Muslims, but his right wing Republican credentials are lacking. That sets him apart from the man who beat him in the Iowa primary: Ted Cruz.

Cruz, who won 27.7% of votes in Iowa on 2 February, on the other hand is a vehemently pro-gun, anti-abortion, Tea Party-esque darling of the Republican right, who has also opposed the resettlement of Syrian refugees in the US and is an outspoken opponent of socialised healthcare. When it comes to policies other than immigration or anti-Muslim fear-mongering, Cruz is every bit the Republican candidate that Trump isn't.

One of Cruz's most famous political moments was the 21-hour speech he gave in 2013 against President Barack Obama's plan for socialised healthcare, which he compared to the fight against the Nazis during the Second World War. The speech was an attempt to "filibuster" the bill – wasting time in order to delay a vote – and included moments of levity such as when he read his daughters a bedtime story and did impressions of Star Wars villain Darth Vader.

He is also a firm opponent of gun control including proposed plans for universal checks on those buying weapons. In April 2015, he appeared before a gun club in New Hampshire arguing against a plan to prohibit soldiers from carrying concealed weapons on military bases after three mass shootings in just five years. He was flanked by his wife, Heidi, who wore a cap that said "Armed & Fabulous".

His social conservatism has him an outspoken opponent of same-sex marriage ("I support marriage between one man and one woman," he said) and a darling of pro-life circles, voting in favour of a bill that would have banned abortion at the beginning of six months of pregnancy. He has not gone as far to suggest an overturning of Roe vs Wade, the case that enshrined the right to choose in law in 1973, but has called its anniversary "dark".

He has been outspoken in his opposition to illegal immigrants and sought to block plans by Obama that enabled undocumented migrants to gain legal status – even in the case of those brought to the US as children. He has opposed any legislation that could have acted as an amnesty for migrants, and once tried to have the number of border guards tripled and their equipment quadrupled. His amendment did not pass.

As for the wider world, Cruz has attempted to outline somewhat of a "Cruz-doctrine" but it has not convinced the pundits. In a statement, he said: "[My] foreign policy strategy follows three principles; Restore leadership on the global stage, rather than withdrawing from it; fiercely defend our allies and interests; Judge each challenge through the simple test of what is best for America, because what is best for America is best for the world."

It has been interpreted as a hands-on attitude with regard to foreign crises such as with Islamic State (Isis) as a counterpoint to the perception that, under Obama, America has receded from the world stage. But critics point out Cruz's tactics for taking on IS (Daesh) in Iraq and Syria do not differ much from Obama's, involving a continuation of air strikes and no US troops on the ground, for now.

But while Cruz remains the darling of the religious right and Trump capitalises the headlines in the modern rhetorical echo chamber, mainstream Republicans may look to Marco Rubio, who only just trailed Trump in Iowa, as a more electable option. As mainstream contenders such as Jeb Bush and Chris Christie fall away, it will likely be those voters that will hold the balance of power.