One day after passing Regulation Best Interest and the agency's four-pronged advice standards package, Securities and Exchange Commission Chairman Jay Clayton took to the airwaves Thursday to explain the difference between "best interest" and a fiduciary standard.

In a Thursday morning interview with CNBC's "Squawk Box," Clayton said that there are all types of "fiduciary" duties, but zeroed in on an investment advisor's fiduciary duty.

"It's a combination of care and loyalty. You owe somebody a duty of care, and you can't put your interests ahead of their interests," Clayton said.

"Best interest on the broker side has many of the same elements, but we want people to understand that the investment advisor space, and the broker-dealer space, are different," he continued. "They're very different in the way people get paid. In the broker-dealer space, you get paid usually a commission on a transaction by transaction basis. In the investment advisor space, it's more of a long-term relationship, where you get paid on a quarterly fee, yearly fee, and the advisor has a more portfolio lifetime relationship with you. Those are two very different relationships and we want to be clear."

The final Reg BI does not define "best interest," which was a major sticking point during the proposal's comment period.

When asked "what this rule [Reg BI] means," Clayton responded: "We're raising the standard of conduct for broker-dealers — the obligations that they owe to their clients."

Second, he said, "we're covering more of the advice spectrum, and one of the things we're covering that's key is account type — when you're rolling over your 401(k) into a different type of account that advice is now covered by our standards of conduct, whether you're a broker-dealer or an investment advisor."

"Before this there was no standard?" CNBC asked.

Clayton responded: "It wasn't clear enough."

Clayton argued that "the power of competition has inured to the benefit of investors so much."

The SEC chairman also challenged the idea that he was stifling innovation in the broker-dealer space by piling on 1,000 more pages of compliance burden.

"I think investors need to know how much of their money is going to work for them. And the key part of this rule package is whether you're an investment advisor or a broker-dealer, you're going to have to be very candid with how you're making your money."

The Financial Industry Regulatory Authority, which will enforce Reg BI, said in a Thursday comment to ThinkAdvisor that "in the coming months, we will be assessing how to conform our rules and examination programs to Reg BI."

Robert Colby, FINRA's chief legal officer, has said that FINRA will either revamp its current suitability rule once Reg BI is final or eliminate it. "There's a lot of overlap between the existing suitability rule and the direction that Reg BI is going in order to mitigate conflicts."