So how can practicing the piano not be playing the piano and vice versa? The really simple answer is that both fulfil a completely different function.
Playing a piece of music really happens once you have learned how to play the particular piece of music. You play a piece of music when you know it quite well and you are playing it because you are playing it for your own personal pleasure or you are playing to an audience.
Playing through a piece of music is also used to check your progress of how well you are learning a piece of music. It will highlight the bits that are working well and it will also highlight the parts that need more practice or are just not working at all.
Practicing can be where you are working on particular sections that need extra attention or new sections that you haven’t really practiced yet. Practicing is also playing the whole piece of music but with intention or a particular focus. For instance it is practicing when you are going from beginning to end focusing on getting the timing correct through counting or using a metronome. Another example is when you are going through the whole piece of music, focusing on getting the loud or quiet parts just so.
Basically, I would say that practicing is when you focus on a section of music or the whole of the piece where your intention is to make improvements to your current level of playing a given piece of music. Playing is where you are checking your progress or enjoying playing the piece of music or playing it for other people.
If you accept this precise definition, then it can help you get the most out of your piano practice. I have had so many students that have debated this with me, thinking that playing a piece of music will yield good results. If you are accurate in your playing of a piece of music, then repetition can help reinforce and consolidate your playing. However, if you are playing a few wrong notes, that you are either unaware of or just haven’t fixed it yet, playing through can actually reinforce those mistakes, which then makes it harder to get it right.
Really when it comes down to it, it is much better to practice a piece of music and get it accurate before playing it. It is also better to be really clear about the distinction I have made between practicing and playing, because that way you can make sure that you are using your time efficiently and if you are learning something new, you can make sure that when you are doing a piano practice you are actually spending that time practicing rather than playing.
Especially when you are in retirement, I think that its really important not just to have piano practice times, where you can learn something new, or improve your technique, but that you have time to play the piano and just enjoy the music you are playing and to also enjoy and appreciate the current skill level you have, whatever it happens to be.