To take you back to basics, if you do the current analysis of an op amp circuit, the polarity of the circuit will naturally affect the output, just make sure you maintain the same current direction you chose for your input impedance across your feedback impedance.
Ex: for inverting resistive feedback op amp, you will have the amp pos input grounded, and the neg input tied to the input via resistor. make a directional assumption( in this case I will say vin > 0), so current of R1 = Vin/R1, meaning current is flowing from Vin toward the output. so the next step would be (0-Vout)/R2 because this is the same direction(right side node subtracted from left side node). combine to get Vin/R1 = -Vout/R2 solve for Vout you get -R2/R1 * Vin, note the sign has followed through. if you do the same analysis for a non inverting amp you will end up with (Vout - Vin)/R2 = Vin/R1, which when solving for Vout you get Vout=R2/R1*Vin + Vin => (R2/R1+1)Vin, note the polarity worked itself out, the trick is to make sure you dont change the direction of your current from your initial guess. Sorry if this was too much back to basics, just didnt want to make any assumptions.
Added quick note, if youre asking about the difference of the positive and negative inputs of the amplifier and why it matters which you connect to, its simply because of the internal workings of the amplifier, a pos change on the pos input will have a positive change on the output, while a pos change on the neg input will have a negative change on the output, due from the current steering in a diff pair(because a single ended output must be pulled off on 1 side of the diff pair ota, assuming single ended output)