A Gaussian refers to a Function that belongs to the parametrized family:

$f\left(x\right) = a e^{- { \frac{(x-b)^2 }{ 2 c^2} } }$

There are also extensions to the case where the input is a vector: Multivariate Gaussian. See this vid (he's missing the determinant of the covariance matrix on the bottom).

The Gaussian is often used to refer to the Normal distribution

https://www.wikiwand.com/en/Gaussian_function

Some probability results for Gaussians