It's similar, but not identical. In CoD, your health recharges over time. In ODST, you have Stamina, and you have Health. You Stamina acts like your shield in Halo 3, so it can recharge in order to protect your health. If your Stamina is down, however, then your health starts to go down. This doesn't recharge by itself, and you need to get a health kit from a health booth, which you can find scattered around the city.
Regards, Chazza1