As the title states, if I load a preset by clicking on it, make changes, and click on Save Changes, it does not actually change the preset.
Instead the current planner is updated. If you then load another preset, you lose the changes. This is counter-intuitive.

I think that is intended. If you want to change a preset, load it, make the changes, enter the name and click the save button in the Preset part of the UI, then save changes.
It's a unintuitive, but i think changing a preset when only applying the changes shouldn't happen (Renaming the "Save changes" button to "Apply" or a green checkmark might make it clearer?)

None of those options make it clear that you aren't applying your changes to your preset. I would suggest you solve it this way: Rename "Save changes" to "Make Planner". When a player clicks on it, it even puts that planner in your cursor, saving you the additional click(s) to get the planner out of the hotbar or Shift-B menu if you're playing with mods. Add a "Save To" button for every existing preset that basically types in the name for you and accepts.
If that's too much of a project, move the text field for the preset saving next to the "Save changes" button and rename the "Save" button to "Save To:", followed by that text field.

I'm planning on giving the gui an overhaul in the next days/week.
It's probably going to end up looking and behaving like AutoTrash (https://mods.factorio.com/mod/AutoTrash) with regards to presets. (Loading a preset puts the name in the textfield, the loaded preset is highlighted etc.)