At a glance
Members. R3 can also change members' ranks.
Officers: recruitment, alliance tech, war declarations, mail, assembly point.
The leader: alliance identity, join requirements, leadership transfer.
Who can do what
R1, R2, R3
View members and leave the alliance. R3 can also adjust member ranks.
R4
Everything an R3 can do, plus: edit the notice, set the assembly point, mail members, open recruitment, remove members, upgrade and recommend alliance tech, manage the banner, declare war, remove reinforcements, abandon a captured city.
R5
Everything an R4 can do, plus: change the flag, name, tag and language, set join requirements, send teleport invites, transfer leadership, disband the alliance.
Officer titles (Warlord, Recruiter, Muse, Steward) are separate from ranks. They mainly show who handles what.
R4s in practice
In most alliances, R4s set targets during the Alliance Duel and sieges, choose which alliance tech to upgrade, and answer members' questions, in game or on Discord. Read your alliance's rules: they are often in the alliance announcement or on its Discord.