The thinking is quite simple.
The U/23's are just a rebranded Reserve team and even though normally full of Academy players anyone can play at that level including senior players. I think the rule is 3-4 players over 23 but in the past you could have a whole team of senior players if you wanted. So 'The Academy' is our U/18 and below.
As mentioned above, there has to be some criteria to categorise who is defined as a youth player and who isn't and to be able to be consistent over time. So generally speaking these three criteria are most commonly used. You have to have had actually played in the Academy, you can't have played professional football elsewhere (you or your team weren't professional at the time) and you must be 17 or younger.
1. If you play in the Academy...then you have played in the Academy by definition. To do so means you are getting coaching and development within that Academy framework. It's like going to a school. You are being educated within that school environment. So you went to that school.
2. If you have played professional football somewhere else then you are good enough to reach the first team. So if you are deemed to be good enough for the first team then most of your Academy development is over.
3. You sign professional terms at 17 and have to be 18 or younger at 1st September to play in the FA Youth Cup. If you are older than this then you are too old for the Academy and Youth football in general. At 18 you are regarded in the world as a an adult. So it's hard to be described as a youth player.
I know UEFA use other criteria but these three have been consistently applied at United and other clubs over many decades.
Here are some examples.
1. Lee Sharpe arrived at 17 (one tick), played in our youth team (two ticks), but was already playing professional football for Torquay when we signed him = 2/3 does not qualify
2. Shaun Goater arrived at 18 (no tick), played in our youth team (one tick), and hadn't played professional football anywhere else (two ticks) = 2/3 does not qualify
3. Amad Diallo arrived at 18 (no tick), played for Atalanta first team as a professional (no tick), hasn't played in our Academy (no tick) = 0/3 does not qualify
4. Rafael & Fabio Da Silva arrived at 18 (no tick), hadn't played professionally elsewhere (one tick), didn't play in our Academy (no tick) - 1/3 does not qualify
5. Regan Poole arrived at 17 (one tick), played in our Academy (two ticks), played professionally for Newport County (no tick) = 2/3 does not qualify
6. Gerard Pique arrived at 17 (one tick), played in our Academy (two ticks), did not play professionally at Barcelona (three ticks) - 3/3 QUALIFIES AS A YOUTH PLAYER
7. John O'Shea arrived at 17 (one tick), played in our Academy (two ticks), did not play professionally for Waterford (three ticks) = 3/3 QUALIFIES AS A YOUTH PLAYER
Some of the other names mentioned like Hoogewerf, Mejbri, Pogba, Rossi and many others all meet the three criteria. So therefore, in very simple terms, they went to our school and graduated from our school as professionals. They then go on to play in the first team of Manchester United or some other club.
Finally, there are quite a few players in the league like Dwight McNeil at Burnley, Jack Harrison at Leeds and many others. These lads were very young when they were at our club and whilst obviously received a lot of coaching in that time...they never reached our U/16's where competitive football really starts. Over the decades lads have arrived at United and played for our U/16's...not younger. Kids could only join at 15. So for consistency purposes I personally use that as an additional criteria. I would argue that Burnley and Leeds respectively, should take the credit for their development McNeil and Harrison into first team players.