I'm looking into using a Gaussian copula to model correlation between two r.v. in a Monte Carlo simulation. I opt for the Gaussian copula as 1) I understand it and 2) it's the most easy one to explain to senior management.
However when reading literature on the subject I got confused. When I read [1, slide 9] it states that "When the underlying cdf is multivariate normal, then the copula is Gaussian", do they refer to the new joint distribution? (that would make sense). In this document [2, page 24 below the Key concept on Sklar’s theorem ] the authors states that you need to estimate the copula's cdf via maximum likelihood (thus making me think I can also make assumptions and just choose one?). Finally when looking at this implementation  it looks like there either are no implicit assumptions or they disregard them.
So my question to you, are there any assumptions that come with choosing e.g. a gaussian or t-copula when simulating correlation of two distributions in monte carlo simulation?
: http://www.stat.ncsu.edu/people/bloomfield/courses/st810j/slides/copula.pdf '' NC state university lecture on copulas"
: http:// www.garp.org/media/691726/quant_classroom_oct2011.pdf "A Short, Comprehensive, Practical Guide to Copulas"
: https://dahtah.wordpress.com/2011/10/28/hello-world/ "Copula's made easy''