Donald J. Trump has said almost too many controversial things to count during the course of his presidential campaign, but over the past few months, one turn of phrase has inspired more online curiosity than fervor: the word “bigly.” Or was that “big league”? Or maybe both?

The phrase popped up on at least four occasions during the three presidential debates, to the delight of many on social media. Mr. Trump has also said it at rallies and in his freewheeling stump speeches.

He has used it to describe how much he wants to cut taxes (a lot); how much he thinks his opponent, Hillary Clinton, will raise taxes (a lot); how many people he says President Obama has deported (a lot); and how many more people Mr. Trump wants to deport if he wins the election (you get the idea).

But what exactly is he saying?

Hope Hicks, a spokeswoman for the Trump campaign, said in an email on Sunday that Mr. Trump had been saying “big league,” not “bigly.” Companies that provide transcripts of the debates have agreed with her, as have many professional linguists, who have been mulling the question for months.