Two organisations counted the same people, which is what makes this resolvable rather than a dispute.

On July 21 ICE published a dataset stating that 39,576 of the 65,765 people in its detention population - 60 percent - 'have criminal convictions or pending criminal charges' [1]. ABC News reported it as 60 percent of detainees having 'a criminal record' [1].

TRAC, which tracks the agency's own records, reported that as of July 11, 46,436 of that same 65,765 - 70.6 percent - have no criminal conviction [2].

Because the denominators are identical, the categories separate cleanly. Convicted: 65,765 minus 46,436 leaves 19,329 people, or 29.4 percent. Charged but never convicted: ICE's 39,576 minus those 19,329 leaves 20,247, or 30.8 percent. Neither charged nor convicted: 65,765 minus 39,576 leaves 26,189, or 39.8 percent.

In plain terms: fewer than three in ten people in ICE detention have been convicted of a crime, roughly three in ten are held on charges no court has resolved, and four in ten have not been accused of anything at all.

More people in ICE detention have never been charged with anything - 26,189 - than have ever been convicted of anything - 19,329 [1][2].

TRAC adds a qualification about the smallest of those groups: among those who do have convictions, many committed only minor offences, including traffic violations [2].

The word doing the work is 'or.' A charge is an allegation the government has made; a conviction is a finding a court has reached. Adding them produces a number that sounds like the second and is mostly the first.