The read-only test only reads. That's basically the default testing method for just about everything and pretty much the same what disks do for SMART self-tests.
The non-destructive read-write test works by overwriting data, then reading to verify, and then writing the original data back afterwards. The only way to verify that writing data works is by actually writing data, no read-only test will ever do that for you.
People who only do read tests (the majority, simply because write tests take at least twice as long) simply take it on good faith that when reading works, writing (and being able to read the data that was written later) will probably work too.
However, the non-destructive is relative... after all the very write itself might destroy it (on a medium with limited write cycles) and once it's broken there is no way to write the original data back either, so even though the test is non-destructive, if your hardware is faulty it might still lose you some additional data.
Therefore you shouldn't use badblocks if there is data on a medium you hope to recover. Especially not if you already know it's going bad... if you don't have a backup already, just do the
ddrescue directly. That also happens to be a read-only test and the logfile will tell you where the error zones are...