In AmE, the morgue is a temporary facility where bodies are kept until they are identified and all necessary post-mortem examination has been completed. The mortuary is the funeral home where the body is prepared for either display and burial or cremation.
By the way, I have two personal questions for you. If you don't feel like them, you can remain silent.
First, what does your alias "Ouisch" indicate? It doesn't sound very English to me.
Second, is it a male or female nickname? I thought it was male, but your gorgeous attractive avatar astonishes me.
As for my screen name, I've been fascinated with "true crime" stories since I was a youngster. One crime saga that I've researched extensively is that of the Manson Family, and I adopted "Ouisch" from one of Charlie's girls (one who was *not* involved with the Tate-LaBianca crimes) because it was unique and easy (for me) to remember. I started using it back in the mid-1990s as an online nickname, and it has stuck ever since then.