Wikipedia, False Statements of Fact, under Remedies, says:
"Punitive damages are sometimes available against an individual who made a public false statement of fact. Criminal liability, although uncommon, can be made although they are usually subject to the same limitations imposed on civil suits in terms of elements to be proven."This sounds very close to a "false factual claim". If a "false statement of fact" is synonymous with a "false factual claim", then both terms describe a false statement which wrongly purports to be a fact. To simply say a "false claim" could, in some contexts be referring, for example, to a false claim over a piece of property.
In other words, what is under discussiion is a "factual" claim, as opposed to a claim on a piece of land, etc..