The phrase "a slightly different purpose" is correct and usable in written English.
You can use it when discussing variations in objectives or intentions in a particular context.
Example: "While the original design was for aesthetics, this version serves a slightly different purpose, focusing on functionality."
Alternatives: "a somewhat distinct aim" or "a marginally altered objective."
There are so many formulas because each is devised for a slightly different purpose, and each uses slightly different calculations and pieces of information to come up with a number, a Pataki administration official said.
The core of the proof is a new notion of k-gradation for P and Q, whose existence (even in an arbitrary metric space) is proved using the Knaster–Tarski fixed point theorem, by a method introduced by Reem and Reich for a slightly different purpose.
"This has the same name but it has got a slightly different purpose," he said.
That said Conferize looks slick and probably serves a slightly different purpose, and it runs automatically whereas Lanyrd is much more manual and only presents links — no previews.
And now those good times live on with the new controller/synthesizer Pianocade, which reincarnates the arcade game-style controller but with a slightly different purpose.
Among my 250 books there are a lot about music in other cultures, as I sensed that it was both organised differently and served slightly different purposes elsewhere.
The use of interviews from two different time periods and conducted by different interviewers for slightly different purposes is an acknowledged limitation of this study.
Since yo-yos have been around for literally thousands of years (they've changed a bit since ancient Greece), a few different kinds have emerged that all serve slightly different purposes: Imperial yo-yos.
Different smugglers use their groups for slightly different purposes.
We were shown three different anechoic chambers, each used for slightly different purposes.
The hole argument was invented for slightly different purposes by Albert Einstein late in 1913 as part of his quest for the general theory of relativity.
