TEGUCIGALPA, Honduras — There are two versions of President Juan Orlando Hernández of Honduras, who is seeking a second term in a country where the idea of re-election is so toxic that another president was ousted in a coup just for talking about it.

The first image is one of a law-and-order leader who pulled his country back from the brink of becoming a failed state. The other picture is one of an autocrat who has imposed his will on every branch of government.

That stark difference in perceptions has turned Sunday’s election into a referendum on how much control over the country’s fragile institutions Honduran voters are willing to cede to Mr. Hernández, a conservative.

“Re-election means the strengthening of presidential rule and an increase in the concentration of power,” said Victor Meza, a security analyst and former interior minister. The result, he said, “could unleash an unchecked authoritarianism.”