Botanical Identity of Mints Used in Vietnamese Kitchens

I'm the author of "Into the Vietnamese Kitchen: Treasured Foodways, Modern Flavors", a cookbook that's due out in October Ten Speed Press. I need your advice on how to botanically identify the mints used in the Viet kitchen. There are several kinds, and I'm mainly concerned with the two kinds that are sold at at Viet markets in the States – one is called h?ng (mint) and the other is h?ng cay (spicy mint). I think that the first one is Mentha spicata (just like stuff sold at regular supermarkets) and the second is Mentha x gracilis, but I'm not sure. In Mai Pham's Pleasures of the Vietnamese Table (a cookbook) and on Gernot Katzer's online spice pages, Vietnamese mints have been botanically identified as Mentha arvensis, Mentha aquatica, and Mentha javanica. Those two sources don't have photos of the mints, which makes my work difficult.
Would you assist me? Can you take a look at the pictures on this page and provide your insights?
www.vietworldkitchen.com/personal/mint.htm
The pictures are of mints that I purchased today. I visited three Vietnamese markets in the San Jose, CA. To compare the h?ng (mint) sold at Viet markets with what's sold at regular markets, I also purchased regular 'mint' (which is spearmint) from an Albertsons supermarket near my home in Santa Cruz, CA. All the h?ng cay (spicy mint) came from Vietnamese markets.

Although it is always difficult to identify plant material conclusively using only photographs, based on my experience with Vietnamese mints sold in the Toronto area I agree that your "h?ng" is a form of Mentha spicata (or possibly of the spicata hybrid, Mentha x cordifolia) and your "h?ng cay" is a form of Mentha x gracilis.
Mint varieties can have highly variable morphologies, scents and flavours. It is possible that mints used in Vietnamese cooking are slightly different from standard varieties. In the case of h?ng, any differences likely are minor compared to our improved spearmint variety. However your description of the scent of "h?ng cay" suggests the variety you purchased is different from the "Vietnamese mint" we offer. Ours has a spearmint flavour and scent but you describe yours as having more of a peppermint flavour and scent. Both can still be Mentha x gracilis despite the chemotype differences.