what is the difference between gaussian distribution and normal distribution
Normal distribution In probability theory, the normal (or Gaussian or Gauss or Laplace-Gauss) distribution is a very common continuous probability distribution. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known.[1][2] A random variable with a Gaussian distribution is said to be normally distributed and is called a normal deviate.
Mean The mean of a probability distribution is the long-run arithmetic average value of a random variable having that distribution. In this context, it is also known as the expected value. For a discrete probability distribution, the mean is given by   ∑ x P ( x )  {\displaystyle \textstyle \sum xP(x)} , where the sum is taken over all possible values of the random variable and   P ( x )  {\displaystyle P(x)}  is the probability mass function. For a continuous distribution,the mean is    ∫ − ∞  ∞  x f ( x ) d x  {\displaystyle \textstyle \int _{-\infty }^{\infty }xf(x)\,dx} , where   f ( x )  {\displaystyle f(x)}  is the probability density function. In all cases, including those in which the distribution is neither discrete nor continuous, the mean is the Lebesgue integral of the random variable with respect to its probability measure. The mean need not exist or be finite; for some probability distributions the mean is infinite (+∞ or −∞), while others have no mean.