"I said to stay back." "I said stay back." What's the difference?

In the 9th episode of Widow's Bay, a woman tells a man beside her to stay back twice. The second time she says, "I said to stay back." I'm wondering why she doesn't say "I said stay back." (She is a native English speaker.) What's the difference between "I said to stay back" and "I said stay back." Thank you.

Syntactically there’s a difference between reported speech and a catenative construction with a to-infinitival.

• Stay back! [imperative]

• I said, "Stay back!". [imperative]

• I said to stay back. [to-infinitival]

But semantically they are pretty much equivalent, with the latter perhaps a little more formal.