Not all the methods in the FAQ below will work for your notebook, but you can just search/run 'msinfo32' or system information to check your bios model and there are other ways to check too.

https://www.asus.com/support/faq/1030673

You may consider the GL702VMK model to be a sub-model of the GL702VM notebooks, so in a way you can consider your notebook to have both model names although the bios model or motherboard may really be the GL702VMK bios or GL702VMK motherboard if that makes any sense.

Or said another way the GL702VMK can be considered to be part of the GL702VM series notebooks although technically the GL702VMK is not an official ASUS model name that is advertised to customers (I consider it to be an internal ASUS model), so you always need to look under the GL702VM models to find it.