The phrase "a different kind of response" is correct and usable in written English.
You can use it when discussing various types of reactions or replies to a situation, question, or stimulus.
Example: "In this discussion, we are looking for a different kind of response that goes beyond the usual answers."
Alternatives: "a unique type of reply" or "an alternative form of reaction."
We have to repurpose vehicles for a different kind of response.
As I pulled together different peace groups, I realised that this particular threat required a different kind of response to most other progressive movements.
While each of these findings leaves room for improvement, they represent a positive reaction from callers who will usually have dialled 999 expecting a different kind of response.
"It's a different kind of response, obviously with the social media and stuff, but you can definitely feel a vibe around him.
Like other recent dramatizations of atrocity, the film, about the 2008 Islamist attacks in India, manipulates narrative tension to excite us, but the bleakness of historical facts produces a different kind of response.
The protests have elicited a different kind of response in Europe, where several food importers have asked U.S. processors to separate and label the engineered beans.
That reality is fuelling a different kind of legal response.
S. aureus is a human pathogen and it can be argued that the CAMPs of animal origin may cause a different kind of transcriptional response than CAMPs of the natural host.
"A feeling of ownership and a sense of responsibility for the care of a plant 'pet' elicit an entirely different kind of response than viewing displays of plants, no matter how spectacular".
Alongside these standard avenues of response in the traditional public sphere of commercial mass media, their regulators, and established parties, a very different kind of response was brewing on the Net, in the blogosphere.
Because of this glimpse of liberalisation, the young generation of dissident writers began to provide a different kind of cold-war response to the earlier pulp-fiction one.
