What a very good question.
IMHO, professional practice makes for a more professional performance. I don't mean a performance for which other people will pay to hear, but one that does justice to the music and the composer's intent.
When I first began playing, I started from the beginning and played to the point where I didn't know it, then I'd attack that hands alone, hands together.
Now (5 years into study), I sit down with the piece first away from piano and analyze as much as I can: where is the fingering going to be challenging, which sections contain technical challenges which I find difficult to master, what at the patterns in the music. Before I touch the piano, I mark off the challenging sections, number the measures, yellow highlight the repeating patterns.
Then, I touch the keys. I start with the most challenging sections, because I'm at the height of my enthusiasm for the piece at the beginning, and each practice session for some time I'll begin with those sections. Everything else comes thereafter.
At the end of every practice session, I'll write out an outline of the next practice session, sequence of pieces, sections and duration of practice. Some days, I just skip the plan, most days I find if I stick to it, I can feel progress.
I'm not a teacher, nor a professional,so I find it is helpful to read books about practice. One of my favorite is "The Practice Revolution."