Would love to help, but unfortunately Lamiacae is not one of my strong families, either in terms of taxonomy or cultivation. I have heard of Vietnamese mint. In fact, there is some in the cocktail of her seeds I tossed into one of the pots on my patio. But this is the first year I have tried it, and I know nothing more about it (and annoyingly the packet of seeds from Baker Creek I used did not have a species name for the stuff.)
One thing it is definitely NOT, based on that picture, is Vietnamese coriander, aka rau ram. That indeed is a different plant. In fact, despite sometimes be referred to as Vietnamese mint rau ram isn't even in the mint family (it's in the Polygonacae, like buckwheat and smartweed).
If it was given to you SPECIFICALLY to make spring rolls, then it could be similar to a kind of Chinese herb called chin jiu which I think is a mint (though it could be a basil, it's been a long time since I saw seed for it for sale) or bai horaphaa (in Thailand). I remember one of my cookbooks saying that, if you couldn't get leaves of that for one of the recipes to use mint leaves.
