The safety pen is a slightly rare and rather strange variant of the fountain pen. Back in the early days of fountain pens, people were apparently nervous of carrying a small jar of ink with them, assuming that it would somehow get loose and run amok. More realistically, there were concerns about the sealing of joint in eyedropper pens. The safety pen was designed to quell these fears (or pander to them, if you prefer) by providing a more demonstrably positive seal on the end of the small jar of ink than existed in other types. This was accomplished by fitting an internal mechanism which lowered the point into the barrel of the pen via the turning of a knob on the tail end, and making the cap fit either flush or actually have a small internal stopper in it which occluded the end of the pen. Sealed!
The problems with this set up were several. The mechanism introduced a seal at the lower end of the barrel which could fail, not unlike the Sheaffer vacuum-fillers of later decades, and that failure could introduce a pen’s-worth of ink to the pocket. If one were not paying attention, it was easy to destroy the point by trying to put the cap on without retracting it into the barrel. The most likely point of disaster, though, were the moments just after removal or just prior to replacement of the cap. When in use, the carriage the point rides in acts to seal the top of the barrel from the inside, and of course the cap takes care of this when in place. During the transition, with cap off and point withdrawn, one is holding an open tube of ink– which if distraction occurs may not remain upright. When compared even to the slip-cap eyedroppers of the early 20th century, this seems to me a much more likely candidate for spillage.
Apart from the sources of worry a safety pen offers, there is also the reduction of capacity attendant on the mechanism. Unlike the standard hollowed-out eyedropper, the safety pen has a fair complexity of material inside the barrel, displacing possible ink capacity.
Filling a safety pen is the same process as filling an eyedropper, except one need only remove the cap; there is no section to unscrew.