Although aware of the subsequent correction from Clinton's spokesperson, defending the original claim of Clinton that Gabbard is a Russian asset, former double-agent Naveed Jamali writes in Newsweek:
On Tuesday, The New York Times changed its reporting to reflect the fact that Hillary Clinton never suggested Tulsi Gabbard is being groomed to be a Russian agent. Rather, in an interview with former Barack Obama campaign manager David Plouffe, Clinton said Gabbard is being groomed by Republicans as a third-party candidate and used by the Russians as an asset.
This fundamentally changes what Clinton was saying from a head scratcher to a head nodder. Clinton is right: Russia is set to interfere in the 2020 elections, and just as we saw with their blind defense of Donald Trump, Republicans are happy to let it happen.
Agents are groomed and directed, while assets are used—often unwittingly. This slight distinction might seem like simple wordplay. However, in the world of espionage, these terms are significantly different. An agent, such as the Russians believed I was for them, is a person who is specifically recruited and then directed to carry out activities ordered by an intelligence service. An asset is a person or thing that an intelligence service can use to its advantage. For example, a candidate who criticizes the impeachment proceedings, supports U.S. withdrawal from Syria, warns of a nuclear arms race and happens to be a presidential candidate would undoubtedly be seen as an asset in Russia's efforts to cause chaos in our 2020 elections. In sum, what about Gabbard wouldn't appeal to Russia? [...]
Is Jamali indisputably correct about his use of the word "asset"? Is there a widely accepted definition of that term in US national security parlance, as documented in some authoritative document, e.g. in some CIA/NSA/FBI manual?
For example, a CIA page, while not defining the term, seems use it only for people who are controlled by the agency's officers or at least in contact with agency's officers for the purpose of providing information:
To be successful, NCS [National Clandestine Service] officers must understand one of the most complex aspects of running assets — human nature.
They do point out that not all assets may be reliable though
NCS officers must understand and assess the intentions and motivations of their assets, as well as the authenticity of the intelligence they provide.
They also mention that there's a class of officers (informally, I presume) called Targeters whose job is to "identifying future assets".
But the CIA generally no longer has a explicit mission subverting foreign governments etc., so the way they define (HUMINT) assets many be too narrow. Interestingly, this page does not use the word "agent" at all; basically in this CIA categorization, there are officers and there are assets.