It turns out that the new two-baht coin is only one of several changes to Thailand's circulating currency. On February 2, the Treasury Department announced changes to a number of coins. The two-baht coin just happened to be the first one released.
The most visible of the other changes (even though these coins are mostly obsolete) is that the 25- and 50-satang coins are now made with copper-clad iron instead of aluminum bronze. The new color looks something like an American penny:
Other changes are less noticeable. The one-baht coin will switch from cupronickel to nickel-clad iron. The five-baht coins will be a hair less thick, and thus will drop in mass from 7.5 to 6.0 grams. The one-, five- and ten-satang coins are also getting minor tweaks, but I'm not even sure why those are still minted at all.
And as with the two-baht coin, it appears that the portrait of the king will be updated on all coins.
I noticed a poster at 7-Eleven that explains the changes. I took a crappy picture with my phone. It's too bad they don't distribute this nice poster as a file on the actual treasury website.