Pointed taps, like stated are for starting or through holes. Flat bottom taps are for blind holes, or holes that do not goo through the part. Once you get into larger sizes though, some may look like a bottom tap but are in actuality a starter tap. The larger ones just don't need the point on it.
Another thing about taps, stay away from 4 flutes. More trouble than what they are worth due to not having enough chip clearance. The best bet for home use, is get two or three flute Gun Taps. I think the three flute gun taps start at either 5/16" or 3/8" in size. Most small 4 flutes, you'll snap them off and they are a real ***** to get out. I've had to remove hundreds over the years for production departments. And if you bind a tap or hear a snap while it's in the hole, good luck on getting one out. They make "tap extractors" but I have never had any luck with them. When you bind and snap a tap, it's stronger than the tap extractor anyways.
And never use a rusty tap. 90% of the time it's dull from rust, or it's an older tap that has been laying around after being used quite a few times. Taps are cheap until you get into the larger sizes. Once you get a tap, don't let them bang around one another and don't loan any out, so you'll always know what you have.