"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 watched with subtitles on.) 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.