The phrase "a different notion" is correct and usable in written English.
It can be used when introducing an alternative idea or concept that contrasts with what has been previously mentioned.
Example: "While many believe in traditional methods, I propose a different notion that could lead to more innovative solutions."
Alternatives: "an alternative idea" or "a distinct concept".
This coronation suggested a different notion of hip-hop royalty.
Women do seem to have a different notion of friendship.
There used to be a different notion of musical culture.
But Germans have a different notion of these.
Besides, you hear, back in 1959 there was a different notion of the regions' potential.
"The visual images gave us a different notion of looking at Ireland's rain front".
Sometimes the reader puts his or her suspicion differently and asks, "Is this word in the dictionary?" Having recently spent a large amount of time researching how a particularly well-known American dictionary was made, I have a very different notion of what a word's presence, or even its absence, in a dictionary implies.
To talk about the form of a judgment will involve a subtly different notion of 'form' than to talk about the form of a linguistic representation.
So the word "occupation" is now occupying the student imaginary, and the prospect of different campaigns physically converging in the square mile on 1 April, and at the University of East London on 2 April, perhaps conjures up a quite different notion of an occupation.
A full triangulated subcategory ({mathcal {D}}_0 subset {mathcal {D}}) in a triangulated category ({mathcal {D}}) is called thick, or sometimes saturated, if it is closed under retracts ([46] has a formally different notion of an "epaisse" subcategory that turns out to be equivalent).
In this paper, patterns refer to a finite family of words (or a regular expression), which is a slightly different notion from that of Position Specific Scoring Matrices (PSSM) [ 10] or in a similar way, from Position Weighted Matrices (PWM) or HMM profiles.
