Normally when you use the terminal to launch a program, if you want to close the terminal, you will have to close the running program as well. For example, the screenshot below is what happened when I tried to close the terminal after I used it to launch pluma:
There is a trick to close the terminal without killing the running program. On the terminal you want to close, just hit Ctrl + z then run the following commands:
disown -h %1 bg 1
After that, you can freely close the terminal without killing the running program.