"Off-peak" is a ticket you can buy at the station on the day (you don't have to buy in advance, although you can if you want to), and is valid for ANY train that runs on that day after a certain time in the morning (7.30, I think - it will certainly be valid on the 10.40).
All Virgin trains from Glasgow Central to Birmingham and London go via Carlisle - what you CAN'T do with that ticket is travel on an East Coast or Cross Country train that goes via Edinburgh and Newcastle. A ticket valid on both the Newcastle route AND the Carlisle route to London or Birmingham would be a lot more expensive.
"Advance" is a ticket you HAVE to buy in advance (you can't buy it on the day of travel) and is valid for ONE specific train only. If you booked an advance for the 10.40 train on a specific day, and you missed that train, it would be tough luck and you would have to buy another ticket - whereas with the Off-Peak ticket, you could just wait for the next train.
Incidentally an Off-Peak Return ticket will always be cheaper than buying two off-peak singles (though not necessarily two advance singles!), and is valid for return within one month - so if you are travelling from Glasgow to "X", and intend to travel back from "X" to Glasgow less than one month later, you may want to buy an off-peak return from Glasgow to X instead of an off-peak single. With return tickets (except day returns, which have to be used the same day!) you don't have to decide the day you're coming back on the day you buy the ticket.
Also if you're booking online I suggest you book directly via the Virgin Trains website, NOT with the rip off website "thetrainline.com" which charges the exact same prices as Virgin then adds its own outrageous "booking fees", "card fees", "collection fees" etc. on top!