The phrase "a different intention" is correct and usable in written English.
You can use it when discussing varying purposes or goals behind actions or statements.
Example: "Her words conveyed a different intention than what I initially understood."
Alternatives: "an alternative purpose" or "a distinct aim".
Some, though, detect a different intention.
He approached this shoot with a different intention: to prove he likes dressing up but doesn't take it seriously.
What we do not yet know is whether a different intention, backed by technologies of precision, will produce a different political result.
The current spring collection, called "The Topography of Globalization," would appear to be his most overtly political — although Im professes a different intention.
But Sean Ellis, founder and CEO of Qualaroo, coined the phrase "growth hacker" with a different intention in mind.
I am simply doing with a different intention.
Although of a different design and with the intention for use only by farmers, it had found its way into regular use because of the parallel functions with bearer Cheques and the exponential rise of food prices.
Mike Ragogna Annee, your latest album, Blue Sky Thinkin', started with a different musical intention until you wrote the title track.
Differences between SAE death rates and those of the efficacy anaylsis are because of a different denominator (intention to treat vs. safety population).
Shook et al. (Shook et al. 2003) suggested researchers should try to examine and integrate different intention models.
Thus, API documentation can be intention-oriented: it may include content for different intention types (general documentation) or different documentations may include content for specific intention types (specific documentations), where they are complementary to each other.
