Short answers, pulled from the story.
Asymmetric federalism is a system in which one or more constituent states within a federation possess considerably more autonomy than the others, despite holding the same formal constitutional status. Symmetric federalism, by contrast, makes no distinction between constituent states, applying the same powers and rights uniformly across all of them.
A federacy is an extreme case of asymmetric federalism, distinguished either by very large differences in autonomy or by highly rigid constitutional arrangements. In an asymmetric federation, all substates share the same formal status and are called "states"; in a federacy, the exceptional unit holds a different label such as "autonomous region."
De jure asymmetry refers to differences in legislative powers, institutional representation, and rights that are written directly into the constitution. De facto asymmetry arises from national policy, opt-out arrangements, and bilateral deals with specific provinces that are not entrenched in the constitution. Canada's federal system combines both types.
Canada's most prominent example is the constitutional requirement that three Supreme Court justices must come from Quebec, while the other nine provinces rely on convention rather than constitutional law for their representation. Quebec also operates its own separate pension plan and negotiated a distinct communique in the 2004 health care agreement, allowing it to apply its own wait time reduction plan and report directly to Quebecers on progress.
Nine of Indonesia's 38 provinces hold special autonomy status. The six Papuan provinces and Aceh gained it due to ongoing or former conflict; Yogyakarta gained it for historical reasons tied to its royal family; and Jakarta holds it because it is the capital city. Aceh's status was a condition of the Helsinki Agreement of 2005, which ended a 30-year insurgency.
Russia's 83 federal subjects are formally equal in federal matters but operate under six different levels of autonomy in practice. Republics are the most autonomous, each holding their own constitution and official language alongside Russian. Autonomous okrugs represent ethnic minorities but lack the right to a separate constitution or official language, while oblasts, krais, autonomous oblasts, and federal cities form the remaining categories.