Context about 22.06.22 change by u/JeffHill

Right click "To deny"

"To deny" big upside: When pulling, accidentally right clicking friendly will not reset aggro.
"To deny" very small upside: you can put summons to follow with right click. With "to attack" you need to use the "Move" command to achieve the same. Objectively better to micro summons with control groups anyway so not very relevant.
"To deny" huge downside: forces an attack command only if the unit is in the deny range, otherwise(if allied creep is 51%+) it executes a follow command: so you will not only run to the 51% creep but also follow them.
"To deny" downside: Have to use "A" to reset aggro

"To attack" upside: will always try to deny creep/summon/player at max range, so as ranged we can spam right click on 51% as ranged without moving towards them. This allows the new last-hitting technique: With "Auto-repeat right mouse" hold right click and spamming S to cancel frontswing until Last Hit HP range. Will not deny ward/tower at max range, will just run towards deniable ward/tower, because only A denies ward/tower
"To attack" upside: will not move ranged hero to the allied creep like "to deny" does
"To attack" upside: can reset aggro with either right click or "A" key
"To attack" big downside: if you misclick friendly, then it just stops at attack range of friendly creep, player, summon but not tower and not ward. If we misclick courier it won't move at all. Solution: when risk of misclicks on allies, use move command. There can be situations where it is impossible to avoid this "misclick".
"To attack" big downside: if you misclick friendly, it will reset aggro which means pulling neutrals, creeps will fail. Solution: when pulling use move command.
"To attack" small downside: if you misclick creep, hero,courier,not tower – we will AA nearest target if standard AA is set. Solution: when risk of misclicks on allies, use move command
"To attack" small downside: Have to use M to put summons to "follow" another summon/creep/player. Objectively better to micro summons with control groups anyway than put them on "follow".

If you tend to misclick on allied creeps/players/summons a lot and don't want to use "Move" command – "To deny" is better. However running to 51% allied creep is NOT preventable.
If you can minimize misclicks on allied creeps/players/summons OR are able to use "Move command" when risk of misclicks is high(like pulling)- "To attack" is better. Misclicks are preventable with "move" command.