Difference between the terms 'joint distribution' and 'multivariate distribution'? I am writing about using a 'joint probability distribution' for an audience that would be more likely to understand 'multivariate distribution' so I am considering using the later. However, I do not want to loose meaning while doing this.
Wikipedia seems to indicate that these are synonyms.
Are they? If not, why not? 
 A: I'd be inclined to say that "multivariate" describes the random variable, i.e., it is a vector, and that the components of a multivariate random variable have a joint distribution. "Multivariate random variable" sounds a bit strange, though; I'd call it a random vector.
A: The terms are basically synonyms, but the usages are slightly different.  Think about the univariate case: you may talk about "distributions" in general, you might more specifically refer to "univariate distributions", and you refer to "the distribution of $X$". You don't normally say "the univariate distribution of $X$".
Similarly, in the multivariate case you may talk about "distributions" in general, you might more specifically refer to "multivariate distribution", and you refer to "the distribution of $(X,Y)$" or "the joint distribution of $X$ and $Y$". Thus the joint distribution of $X$ and $Y$ is a multivariate distribution, but you don't normally say "the multivariate distribution of $(X,Y)$" or "the multivariate distribution of $X$ and $Y$".  
A: The canonical textbooks describing properties of the various probability distributions by Johnson & Kotz and later co-authors are entitled Univariate Discrete Distributions, Continuous Univariate Distributions, Continuous Multivariate Distributions and Discrete Multivariate Distributions. So I think you're on safe ground describing a distribution as 'multivariate' rather than 'joint'.
Conflict of interest statement: The author is a member of Wikipedia:WikiProject Statistics.
A: I think they are mostly synonyms, and that if there is any difference, it lies in details that are likely irrelevant to your audience.
A: 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 $p(x) = N(x ; \mu, \sigma)$.
A multivariate normal distribution has mean vector of length $n>1$ and a covariance matrix of size $n \times n$. For two univariate random variables $x,y$ they can be jointly distributed according to a multivariate normal distribution $p(x,y) = \mathcal{N}([x \ y]^\intercal ; [\mu_x \ \mu_y]^\intercal , \Sigma_{xy})$.
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, $p(x,y) = N(x ; \mu_x, \sigma_x)*N(y ; \mu_y, \sigma_y)$.
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
