This may be an obvious question but what does "export video" actually mean? does it get shared anywhere online? or is it just to save the file on your computer?
I've not got MET2 to check, but it seems from the original version and in comparison to other Magix products, that 'Export' is the option for creating a file which is saved on your computer to do whatever you want with it later. The term 'Publish' generally refers to the options for creating an output file (presumably also on you computer HD at first) which is automatically used elsewhere eg as an e-mail attachment or sent to a social media site like Facebook.
No doubt others will be able provide more information.
Carl is correct when he says . . . . 'Export' is the option for creating a file . . . . the file in question is a complete video of all the clips / images and audio you have added to the project that is saved on your computer.
With the free version you have only 2 format options - mp4 or wmv video.
What you do with afterwards is entirely up to you, however if you intend to share this and have it play on mobile devices then you should export as mp4.