The phrase "a different type of relationship" is correct and usable in written English.
You can use it when discussing various forms or categories of relationships, whether personal, professional, or otherwise.
Example: "After years of friendship, they decided to explore a different type of relationship."
Alternatives: "a distinct kind of relationship" or "an alternative form of relationship".
While the contestants on "American Idol" form an emotional connection with the show's viewers, it is a different type of relationship.
I thought this story was really interesting, and I loved hearing about a different type of relationship!
"It's not a radical break, but it's one that I think offers us the chance for a different type of relationship, and this nuclear deal, I think, is a potential expression of that".
And it could potentially open the door to a different type of relationship between the United States and Iran that, in our view, could be very healthy for the region".
However, this could generate important biases if the actual network is different to that observed, either due to measurement error or because a different type of relationship is the relevant one for mediating a particular effect.
Michaels and Johnson say that this would be an illustration of a new frontier, a different type of relationship.
Coaches develop a different type of deep relationship with their players because of the commitment and accountability it takes to be part of a team.
Structured prevention – which necessarily involved more communication, education and skill development in patients – instituted a fundamentally different type of relationship between dentists and patients.
Richard McGee wanted to create a different type of mentor-mentee relationship.
A recent study suggested that men in the U.S. may not pay for sex outright as much as we think, but how many of them are entering into a different type of personal bartering relationship with women?
Yoko had conceived the relationship between Caim and Angelus as a parasitic one, with Caim as the host, but Iwasaki wanted to create a different type of romance and instead wrote their relationship as a love story.
