I’ve not worked with splines much, but @paul.buerkner will surely be able to explain this to you. I checked the help pages for these two functions and I can’t find a description of the y-axis per se, but in conditonal_effects() Paul write that it provides a data.frame containing: ‘predicted values of the response.’
conditional_smooths shows thinks on the link scale, that is, logits in this case. No way to change that right now. conditional_effects also adds the intercept, hence the difference uncertainty.