To be sure, the two countries have "distinctly different approaches to influence" operations, Timothy R. Heath, a defense analyst at the Rand Corp., said in an email.
But they are often linked in reports on authoritarian governments' foreign influence campaigns and by senior American defense officials.
President Donald Trump's 2017 National Security Strategy notes that "China and Russia want to shape a world antithetical to U.S. values and interests."
In a speech last week at the 2018 Shangri-La Dialogue, Defense Secretary James Mattis noted that while he believed the two countries had disparate interests, "[T]here may be short-term convergence in the event they want to contradict international tribunals or try muscling their way into certain circumstances."
China has been accused of increasing its espionage operations in the United States, as well as restricting its citizens' access to Western media and harassing or detaining U.S.-based journalists. Beijing has also faced criticism from human rights advocates over accusations that it has intimidated Chinese college students studying on American campuses and pressured them to toe the Communist Party line.
"The Congress and the American public need to better understand the malign goals of China's political influence operations, identify the key institutions, entities, and individuals that carry them out, and distinguish them, if possible, from the cultural, educational, and people-to-people exchanges which benefit both the American and Chinese people," Smith, the bill's sponsor, said in a statement.
Some in Washington are reluctant to tie the increased interest in China to Moscow.
"I'm sure you'll get multiple answers, but this interest would be occurring the same way regardless of the externality of interest in Russia," Jason Thielman, Sen. Steve Daines' chief of staff, told CNBC. Daines is a commissioner on the Congressional-Executive Commission on China, a government group that monitors China and is chaired by Smith and Rubio.
The recent interest in China "has a China-specific trajectory here that was already well underway before Russian interference in the 2016 election," said Andrew J. Nathan, a professor of political science at Columbia University.
That trajectory can be traced back to the Obama administration, Nathan said, and its acknowledgment that "engagement hadn't worked."
The congressional aide who said the recent legislation was accelerated by the "Russia stuff" agreed that it was also an acknowledgment that "the engagement theory had been discredited."
The engagement theory refers to the accommodative policy toward China taken by U.S. presidents from Richard Nixon to George W. Bush, typified by Nixon's visit in 1972 and the admission of China into the World Trade Organization in 2001.
The Senate and House bills are both expected to have bipartisan supporters. The House bill is co-sponsored by five Republicans, including House Freedom Caucus Chairman Mark Meadows, and one Democrat, Rep. Marcy Kaptur of Ohio.
As recently as Wednesday, Rubio has been looking for a Democrat to co-sponsor the Senate bill, the congressional aide told CNBC, though it is not clear which Democrat might do so.
Likely candidates include the three Democratic senators who serve as commissioners of the Congressional-Executive Commission on China, including Sen. Gary Peters of Michigan, Sen. Dianne Feinstein of California and Sen. Jeff Merkley of Oregon. The senators did not respond to requests for comment from CNBC.