Silence
Silence is one of the disable effects in Dota 2 that makes you unable to use the spell for the duration of silence. But enemies affected by the silence effect can still move, attack and use passive items and skills not exposed to silence.
Examples of spells that have silence effects are Global Silence, Gust, and Crippling Fear.
Mute
The workings of the mute as a whole are almost the same as silence, which distinguishes them from the effects of mute making you unable to use items as well.
Examples of spells that have a mute effect are Doom and Static Storm that have been upgraded Aghanim's Scepter.
Break
Break will give a disable effect that makes passive ability (passive skill) not working. In general, almost all passive skills can be disabled by break. But there are some non-disabled passive skills like Reincarnation and Requiem of Soul.
Break also does not disable passive skill synergies with other spells of heroes, such as Grow which affects the damage from Toss. Break also does not make the passive skill on the item affected disable.
Examples of spells that have a break effect are Silver Edge, Doom who got upgraded Aghanim's Scepter and Demonic Purge who got upgraded Aghanim's Scepter.
Forced Movement
Forced Movement is one of the disables, the affected unit will be forced to migrate and keep you immobile for the duration. Some spells even make you unable to attack, use items and use spell during duration of forced movement.
Root
Root (formerly called ensnare) is one of the disable in Dota 2 that keeps root-affected units immobilized and uses multiple spells like Teleportation and blink from Blink Dagger, Anti-Mage and Queen of Pain. But units affected by root effects can still turn around, using spells and items. Some spells that have root effects also make the unit unable to attack (disarm).
Image Source: Dota2.