There have been a couple of hard disk erasing apps on GOTD recently. We've also had file recovery apps offered from time to time. The basis for hard disk erasing software is to make sure those file recovery apps won't work. That means zeroing out every bit of storage on the drive. An article by Ed Bott brought up a point I thought interesting -- encrypt the drive, then format it or delete the partition, and anything remaining on the drive would be gibberish. The free open source VeraCrypt can be run portably, so you could boot to a USB stick/drive, encrypt the hard disk, clear the drive, then reinstall Windows for example. zdnet[.]com/home-and-office/work-life/wiping-a-windows-laptop-heres-the-safest-free-way-to-erase-your-personal-data/
The principle of secure erasing software is to go beyond that however. A conventional hard disk stores data magnetically on rotating platters, with read/write heads floating barely above the platters' surface. Think of a record player or phonograph. Those floating heads have a tiny bit of wiggle room, so they may write a bit to the left or right, and so writing over any data *might* leave something at the margins. The average person could not access that, but a tech specialist with the right equipment might. SO, erasing software overwrites everything multiple times, based on the theory that at least once the write heads will veer all the way left, and in another pass, all the way right.
Though the Trim command zeros out any previously deleted data on an SSD, clearing all data can be a problem, because there's extra storage capacity that can be rotated out of service, as part of a wear leveling scheme carried out by the SSD's firmware. Zeroing out the *available* storage will not touch that extra storage. SSD manufacturers *may* provide a command &/or software to return the SSD to an as new state, but it may or may not work. Best bet is to Google using the make & model of your SSD for real world info -- the only way to make sure data is irreversibly gone may be to physically destroy the drive. That does Not mean the average person can get anything usable off an SSD that's been cleared -- an experienced electronics tech *might* access the individual memory chips to try to exfiltrate data.
Businesses might use hard disk shredding services, while the average person may just try to destroy an old drive, especially if it failed so they couldn't try to delete anything. Again, the average person isn't going to get anything off a drive that's been zeroed out or is inoperable, but if you're worried about someone going to extremes to recover your data, bear in mind how they'd go about doing so. To prevent someone probing the individual memory chips in an SSD, I'd imagine those chips would have to be destroyed. To prevent someone from reading magnetic traces on a hard disk platter, I'd guess that platter would need to be destroyed. I doubt simply damaging the housing or casing would do more than discourage the average person from plugging it in to see if there was anything there.