(CNN) Justice Department special counsel Robert Mueller's double-barreled court actions on Monday have revved up talk of possible "collusion" between Donald Trump's 2016 campaign and Russia. But as those filings suggest, cases are likely to be built on less sensational sounding charges, such as making false statements.

There is no actual federal crime of "collusion" in this kind of investigation, even though the word is popularly used to describe possible complicity between Trump associates and Russian operatives who tried to influence the 2016 presidential election.

Trump himself invoked the word "collusion" in a tweet on Tuesday related to the indictment of his former campaign chairman Paul Manafort, declaring that Manafort's lawyer said "there was 'no collusion' and events mentioned took place long before he came to the campaign."

In fact, Manafort and former Trump campaign official Rick Gates were charged with 12 counts tied to, among other offenses, unregistered lobbying with a foreign power and money laundering. They have pleaded not guilty. Many allegations date back years before the 2016 campaign, yet the two men are accused of laundering money through US and foreign corporations and bank accounts into 2016.

Separately, new public documents show that former Trump campaign adviser George Papadopoulos pleaded guilty to lying about his contacts with people connected to Russians who wanted to offer the Trump campaign "dirt" on 2016 Democratic nominee Hillary Clinton.

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