In the definition of indistinguishability obfuscation (iO), we have a probabilistic algorithm Obs that receives as input a circuit C, such that $i)$ the output Obs(C) is a circuit with the same functionality as C and $ii)$ for any $C_1$ and $C_2$ with the same functionality, we have that Obs($C_1$) is indistinguishable from Obs($C_2$).
Has a similar notion (and candidate construction) for a similar concept where the security holds for $C_1$ and $C_2$ are almost the same (i.e., they agree on all except a negligible fraction of the inputs, and it is computationally hard to find the points where they differ).