That’s not a real distinction. Hank is a DEA agent conducting an investigation. In this case he’s conducting a secret investigation and asked Jesse for a confession when he hasn’t been charged and hasn’t been advised of his rights. Emphasizing that I’m not a lawyer… I find it just about impossible to believe that it would be legal. Jesse confessed to murdering Gale and who knows how many other crimes on that tape. How would anyone use that in a trial? It might give the DEA a starting point as they investigate Walt, but then they’d have to hope nobody found out about the circumstances of this confession. To me this is relevant because we can be pretty sure Walt doesn’t get convicted of anything.
Hank wasn’t worried about Jesse’s safety- he made that very clear later. He was doing this off the books because he knew Walt would find out if Jesse had been arrested, and this way Walt can’t destroy any evidence.