The Hopkins MPH has changed in the past few years but the deal is, more or less, that the MPH is a masters in public health and is not specific to any department, although now you do define a concentration in a department. The MHS is a masters degree conferred by individual departments and has different requirements by dept. For Epidemiology, you have to do a thesis, although I think it can be a library review or very basic analysis. More in-depth data driven theses will get you an MSc (Masters in Science).
Having worked overseas, I thought the MPH was more recognizable but among those in the field, the MHS works just as well. The MPH is more of a generalist's degree. Most importantly, the MPH at Hopkins is one (*intensive*) year while the MHS degrees can be 1 or 2 years, depending on department. Also, the MPH program requires at least two years professional experience while the MHS degrees generally do not.
Long winded, sorry- its late...