There are different types of silent protagonists ranging from characters who cannot or will not speak to those who are simply never depicted as speaking.
See also: Silent Protagonists Who Talk in Sequels.
Mutes are characters who are recognized within the game world as people who are incapable of speaking. Claude Speed from Grand Theft Auto 3 is considered a "mute." However, some characters are mislabeled as mute because their character does not say anything. For instance, the Space Marine from the original Doom is not considered a mute, since he is never given a reason to speak, so it's unknown whether or not he can.
See also: Mute character.
Secretive silent protagonists are protagonists who do have any written speech, but other characters within the world act as if the protagonist can speak or have spoken in the past.
Secretive protagonists can exist in an entirely linear game without compromising the ability of the player to insert themselves onto the character. They can also possess background information, even a personal history, and still remain open for the player to establish a personal connection. For example, Gordon Freeman of Half Life 1 and Half Life 2's never speaks a word during the gameplay, yet is treated by his companion Barney Calhoun as a drinking buddy and partner. Silent player characters in many JRPGs, such Suikoden V and Persona 4, are secretive in that they rarely or never directly assert themselves, yet are treated as the center of the game's storyline and as primary decision-maker.
Games with secretive protagonists sometimes force writers not to assume a player's reaction and instead have NPCs react to themselves. For example, when Alyx of Half-Life 2: Episode 1 coins the term "Zombine," her character does not assume that Gordon laughed or did not laugh, instead she reacts to her own bad joke, regardless of whether or not the player (as Gordon) thought it was funny.
Reactive silent protagonists are protagonists whose actions are assumed by the game's scripting, but do not have written lines or dialog options. Other characters in the world react to player as if they have spoken but the words are never shown or heard.
Link from The Legend of Zelda series is considered a "reactive" silent protagonist. In Ocarina of Time, Princess Zelda asks Link what his name is, and while no dialogue circle appears indicating that Link has spoken, Zelda replies "Link??? That seems familiar," implying that he has said something.
The "Commander" personality addressed in the FMV cutscenes of the Command & Conquer series can be considered a reactive silent protagonist because the character is directly addressed by the onscreen NPCs. Their reactions are assumed automatically to agree with, or submit to, the demands and motivations of the NPCs.
A reactive silent protagonist is essentially a prescripted character whose lines of dialog have been removed.
In some instances, games subvert the silent protagonist concept by blending the concepts as a plot point. The protagonist of Bioshock, Jack, appears to be a Secretive silent protagonist, but late-game events reveal otherwise.