Well, there are actual, measurable, physical differences between the three types:
Early 400K disks were truly one-sided. There was no magnetic coating on the other side! (Unlike single-sided 5.25" disks, which often had the coating on both sides, just in case someone tried to use it 'upside down', which is impossible with 3.5" disks.)
"Good" single-sided drives should never destroy a double-sided disk, because they just have a felt-covered pressure pad opposite the read/write head. Unless the pressure pad breaks, a double-sided disk should work just fine (when formatted as single-sided,) in a single-sided drive, and back again.
The move to high density, however, presented problems. High density disks use a much weaker magnetic field than low density disks. If you use a "High Density" disk that has never been formatted in an 800K (properly called "Double Density", but more often called "Low Density",) drive, it will likely format just fine. The stronger magnetic field of the 800K drive may not 'hold' for as long as the weaker magnetic field that the HD disk was designed for, but it should work for short-term uses.
The problem arises that once you have done that, an HD drive doesn't always have enough 'oomph' to negate the DD format completely. This means that re-formatting an HD disk to HD can fail, and essentially ruin the disk for any future use.
Likewise, an 800K disk is meant for the stronger magnetic field, and often had 'coarser' particles that may not even be tightly-packed enough to be formatted as HD, even if the disk had never had a DD format done to it.
In short: 400K disks should always assumed to be purely one-sided, and never attempted to be formatted as anything else. 800K disks can be reformatted as 400K and should have no problems whatsoever (unless you put it into a 400K drive that is physically broken so that it scratches the 'back' side.) 800K disks that have never been formatted (especially later-manufactured ones,) CAN be formatted as HD, and then re-formatted 800K again, but formatted 800K disks should never be re-formatted as HD. HD disks can be formatted to 800K, but it can be unstable, and once formatted as 800K, will be VERY unstable upon re-formatting to HD. But, HD 3.5" drives should be able to read and write (and even format,) 800K and 400K disks with no problems whatsoever, because HD drives can do both strengths of magnetic field, when they know which strength to use.
The problem with 5.25" disks and drives is that most HD drives didn't have the ability to operate at the stronger field strength of lower-density disks. This meant that a 360K disk that was formatted on a 1.2MB drive may work just fine in 1.2MB drives, but not in native 360K drives. Reading was usually not a problem, only writing.