I'm not quite sure what bioinformatics is exactly, but I did do a bit of work on genetics data during an internship at the CDC. From my point of view, biostatistics is not bioinformatics. Biostatisticians and statistics as a whole are a large field, but there are definitely some people that intersect with the informatics realm. It's definitely not an area everyone works in though. If you're interested in genetics, and looking at biostatistics programs. I highly recommend Columbia's biostatistics PhD program. I interviewed there, and they had a very large focus on developing methodology for analyzing genetic data. I ended up choosing another program because I wasn't particularly interested in that area and I wanted to do a pure statistics PhD. However, it seems like you'd like it quite a bit.