The SSD1306 does not handle different sizes, it's ever only handling it's maximum size 128x64. But one can decide to only use less pins of the driver for a smaller display.
The SSD1306 has 128 segment pins, which activate the current column, so that the states of the 64 common signal pins will be used by the display for that column. For smaller display sizes there are just some pins of the SSD1306 left unconnected. They get set like all the other pins, but they are not connected to anything, thus the information gets lost.
For accommodating that, the library sets the pixel according to the size by not using every second row (aka common signal) for half size displays. That's why you get horizontal black lines, when using a 128x64 display with the library in 128x32 mode. The library thinks, that every second row is not connected either way and thus sets these pixels to black. The 128x32 display is loosing every second row when used with the library in 128x64 mode, because every second row is not connected.
Note, that nor the library neither the SSD1306 know about how the display is connected. You need to tell the library this, by setting the mode, and it will control the SSD1306 accordingly. So there is no feedback about the display, that you could use.
Can I expect that, at least if I use the same driver library, that using the wrong screen will always have this behavior?
Yes and no. The library handles it this way, because it is the common way to leave out every second pin for displays of half size. But it comes down to the manufacturer to decide this. We cannot guarantee, that nobody will ever connect the SSD1306 in a different way to a display.
For most manufacturers you will be good. If you simply plan to provide the displays for your user, so that they can change them their selves, you can be sure. If the user should be able to use her/his own display, purchased anywhere else, you might run into problems (though rarely).
