Most, but not all cylinder records used variations in groove depth to drive the needle vertically. That was more efficient when the only "sound equipment" consisted of a diaphragm attached to the needle and a large horn. With the advent of electronic amplification, which came along by the early thirties, the 78s used a constant width, constant depth groove that "wiggled" the needle side to side. The sides of the needle had a very small (usually 7-10 degree) "wedge" and the tip was a fairly large smooth "ball" that rode in the bottom of the groove.
For a microgroove recording, generally 33-1/3 rpm, the needle has a 45 degree slope on each side, and a very small tip radius that should never touch the bottom of the groove.
When a microgroove needle is used on a 78 rpm record, the 45 degree "flanks" of the needle allow it to wedge into the groove and scrape the tops off. Wear of the record can be quite rapid if this happens. Many 78s have a wide enough track to allow some microgroove needles to go all the way to the bottom, where the tiny tip radius acts like a high speed lathe tool to cut the bottom out of the groove. Once you cut through the vinyl/shellac (whichever) in the bottom of the groove, many 78s have a clay or paper, sometimes with added asbestos, "core" that is permeable to moisture, and once it's exposed to the air the whole surface of the record may start to "spall off."
Playing a 78 with the wrong needle once or twice to see what you've got or to transfer to another medium probably isn't likely to cause discernible damage, but if you intend to play 78s repeatedly it is advisable that you match a "78 needle" to the disks - and use it ONLY for the 78s. (Inadvertently putting a microgroove record on under the "78" needle may cause a lot more damage to the record than a limited use of the microgroove needle on a 78 record.)