Here is a brief overview of how the minor league classifications work:
Currently there exist the following designations:
AAA (highest classification)
AA (second highest classification)
A - Advanced (also called High A) (third highest classification)
A (also called Low A) (fourth highest classification)

I'll give a brief history of classifications as well...

In 1902, the National Association of Professional Baseball Leagues was formed and existed with the following classifications from highest to lowest:
A, B, C, D

In 1912, the classification of AA was established as the highest classification, the system was as follows:
AA, A, B, C, D

In 1936, the classification of A1 was established which was between AA and A, creating:
AA, A1, A, B, C, D

In 1938, the classification of E was established to be the lowest classification (the only Class E League - Twin Ports League (1943)):
AA, A1, A, B, C, D, E

In 1946, the system was restructured with AA leagues becoming AAA and A1 leagues becoming AA:
AAA, AA, A, B, C, D, E

In 1952, the classification of Open was established for the Pacific Coast League to help it become a major league:
Open, AAA, AA, A, B, C, D, E

In 1958, the classification of Open was removed when the National League moved into Los Angeles and San Francisco:
AAA, AA, A, B, C, D, E

In 1963, the system was radically restructured as follows:
AAA (highest classification)
AA (second highest classification)
A - Advanced (also called High A) (third highest classification)
A (also called Low A) (fourth highest classification)
A - Short Season (fifth highest classification)
Rookie (lowest classification)

In 2021, the leagues were reclassified to its current configuration and 43 teams were contracted (with 3 new teams being added).
The A - Short Season and Rookie levels were eliminated resulting in the contraction of the NY-Penn, Appalachian, and Pioneer Leagues.
The California and Florida State Leagues were reclassified as A from A - Advanced.
The Midwest League was reclassified as A - Advanced from A and the Northwest League was reclassified as A - Advanced from A - Short Season.

Questions or comments...e-mail me.