you could say "60" refers to the timebase in Hz rather than the framerate.
then the p or i denotes whether this timebase is expressed in fields per second or progressive frames per second.
60i is the standard way of saying 30fps, interlaced. it's not just marketing bunk either, as the EBU and SMPTE standards also use this terminology.
@ johnmeyer: the last bit of kine i transferred must have been done on a newer machine. fields were visible when i zoomed in my TK, but i didn't have enough time alone with the film to try to line it up perfectly. also, there was natural blurring, probably in the lens used (it was gaussian-ish). weave isn't too bad on modern cameras, and not a problem at all with pin-registered scanners (unless the film is still soft from cleaning). but of course not much kine has been done with modern cameras
the most recent bit of kine i can think of is the TV series "Frontline", where the documentary-style bulk of the program was shot on hi8 and kine'd to 16mm, then TK'd back to beta SP... sort of like a very expensive deinterlace.