While both of these commands will tell you if your new nginx configuration is ok [without killing your current instance]. Configtest uses the running service and tells you if it passes or fails the check whereas nginx -t will not only check the config but print any info, warning as well as error messages..
Usage is typically:
service nginx configtest && service nginx restart or nginx -t && service nginx restart
My personal preference is to use nginx -t because 1. its shorter and i’m lazy snf 2. I like knowing where exactly the problem lies (easier debugging and whatnot).