Half Elves can be born from two Half-Elf parents, or from having one parent be a Half-Elf, and the other a Human.
Although it isn't an option presented in the book, you might also have a Half-Elf born to two Human parents who both had Elven ancestry (but not enough for them to present as Half-Elves).
It's not the same as Tiefs and Aasimar, they are planetouched, which means they either have a planar creature in their ancestry, or someone in their family was warped by planar energy. In Pathfinder and to a lesser extent D&D 5e, you could have spontaneous planetouched, which includes planetouched babies being born to non-planetouched parents because of high levels of planar energy in the environment they live in.