What is the phrase I'm looking for?
A-Order |BKGS|XQYU|QZGU|QTMS|DCRH| 33141 |DSBC|QBLS|YHPL|RHXP|AQPN| 32413 |RTEQ|YEVS|LMHR|IOPU|IMVB| 21342 |HJOP|FRWA|AMLA|BONZ|TYVP| 23123 |QRWF|ZUFE|YUIS|WIUB|ARTO| 42212
One letter per box.
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The phrase you are looking for is:
(a square containing a number of integers arranged so that the sum of the numbers is the same in each row, column, and 2 main diagonals, as alluded to by: | (vertical), X (diagonal), and - (horizontal) which are in the top parentheses.
We note that (as @new QOpenGLWidget posted) "A-Order" likely means
"alphabetical order", and the digits matching the 5 columns with values from 1-4 suggest we take the nth item from each 4 digit value in the corresponding column.
Converting to numbers yields:
11 24 7 20 3
4 12 25 8 16
17 5 13 21 9
10 18 1 14 22
23 6 19 2 15
Which is a MAGIC SQUARE where each row, column, and diagonal sum to 65. (12 sums in total, so "All twelve the same" as stated in the title!).
A partial answer.
"A-Order" seems to mean alphabetical order, so let's order our words in alphabetical order.
|BGKS|QUXY|GQUZ|MQST|CDHR| 33141 |BCDS|BLQS|HLPY|HPRX|ANPQ| 32413 |EQRT|ESVY|HLMR|IOPU|BIMV| 21342 |HJOP|AFRW|AALM|BNOZ|PTVY| 23123 |FQRW|EFUZ|ISUY|BIUW|AORT| 42212
Now use the numbers on the right. So we get
|K|X|G|T|C| |C|L|S|H|N| |Q|E|M|U|I| |J|R|A|N|V| |W|F|S|B|O|
...which, unfortunately, doesn't have anything too useful. I've tried a Caesar cipher, but it doesn't work. I'm thinking about trying a Caesar cipher on the box, then doing the steps above.
I also don't know how (|X-) or "All twelve the same" figures into this.