This is standard for any play — if a show runs long enough, several actors play the same character. This leads to intense debates about which actor or actress is the "best".
Bears mentioning here that it happens quite regularly in plays where the understudy steps in due to illness, vacation, etc. of the main performer.
One very notable case is Agatha Christie's play The Mousetrap which has been running continuously for literally decades leading to actors who have played younger characters in the show taking over the roles of older characters as they've become too old to play their younger characters.
Shakespearean actors have been known to do this as well—Ellen Terry, for example, played the Prince of Sicilia in The Winter's Tale at age eight, and later in life appeared as Hermione in the same play.
Many cast recordings of musicals have used different singers, with the regular actor being unavailable due to contractual reasons (e.g. Irra Pettina replaced with Kitty Carlisle on Song of Norway, Ethel Merman with Dinah Shore on Call Me Madam), illness (Howard da Silva replaced with Rex Everhart on 1776), or having too small a singing part to bother (in which case another cast member usually would fill in). One unusual case is the original cast recording of Company being reissued on LP with Larry Kert (who replaced Dean Jones shortly after the Broadway opening) overdubbing all of Dean Jones's vocals. In a bizarre case of crosscasting, Gabey's two solos in On the Town were sung by Mary Martin (substituting for John Battles) on the original cast album.
Aversion: While much of the Broadway cast of The Phantom of the Opera has changed greatly since its original 1986 run, the actor playing Firmin remained the same up until 2012.
Although the long run at Toronto's Pantages Theatre did change leads, notably featuring KISS's Paul Stanley, who returned for the final two weeks of performances due to patron demand.
And played straight with the role of Christine, which is so taxing that an "alternate" actress is cast to handle two of the eight weekly performances.
Some runs of the The Producershang a lampshade on this. Tony Danza at one point played the part of Bialystock, who in the script is insulted by Leo Bloom as "FAAAAAAATTT!!" When the line came up with Danza playing the part, the decidedly trim Danza responds, confused, "What?" Leo then, somewhat uncertainly, asserts, "You ... used to be fat..."
Some shows deliberately change a character's actor mid-season, others will alternate between actors, as ACT does with Scrooge in their annual production of A Christmas Carol.
Averted by William Shakespeare. When comedian Will Kemp left Shakespeare's company, the clown or jester characters in Shakespeare's subsequent plays have a noticeably different tone, as they were written with the darker, more cerebral style of Kemp's successor, Robert Armin, in mind.
In A Very Potter Senior Year Meredith Stepien replaces Bonnie Gruesen (from the first two installments) as Hermione. Of course, in true Star Kid fashion, it's lampshaded. Hermione breaks her nose at the beginning of the musical and fixes it with a spell, but looks different.
Hemione: Well, I may look different, but you guys should just treat me like I'm the same old Hermione you know and love. (To audience) And that goes for all you too. (She winks at audience)
This may sometimes happen if a show moves theatre or does a tour in a different country; one or two actors may retain the same role, but the rest will be more local.