Not really. Jeopardy, danger and peril are pretty close synonyms. To put your King in danger is more immediate and dire than to place him in jeopardy. Walking him toward the center in middle game puts him in danger. Leaving him alone on the back rank might put him in jeopardy. The distinction is quite slight, though.
Incidentally, "place" goes with jeopardy, and "put" goes with danger.