Yes OfficerKite, once you pass positively the BAA selection they will propose you to both in theory...in practice, from what I have experienced, I think they send your package and test results to the airline that best fits with your curriculum, previous experiences, competences (especially soft skills) and airline values, vision and core business.
Just to give you an idea, SmartLynx is fully embedded in the ACMI business, that differs quite far from a "routinary" airline like Wizz or EZY, (nothing wrong, just a different work regime with different needs in terms of crew mobility, seasonal bases, short term allocation as needed and alike), having said that also the would-be-cadet profile that best fit-for-purpose their desiderata plays an important role in the allocation of slots among the 2 schemes.
Hope this helps and good luck to all.