I would be careful to say a joint distribution is synonymous with a multivariate distribution. For example a joint normal distribution can be a multivariate normal distribution or a product of univariate normal distributions.
A univariate normal distribution has a scalar mean and a scalar variance, so for the univariate (one dimensional) random variable x distributed according to a normal we have p(x)=N(x;μ,σ).
A multivariate normal distribution has mean vector of length n>1 and a covariance matrix of size n×n. For two univariate random variables x,y they can be jointly distributed according to a multivariate normal distribution p(x,y)=N([x y]⊺;[μx μy]⊺,Σxy).
However, if the covariance matrix of the multivariate distribution is a diagonal matrix, this means that x and y have zero correlation (are independent) and so the joint distribution can be a product of univariate Gaussians, p(x,y)=N(x;μx,σx)∗N(y;μy,σy).
Therefore the joint distribution is not really synonymous with the multivariate in the case of independent variables.
https://en.wikipedia.org/wiki/Joint_probability_distribution#Joint_distribution_for_independent_variables