Does a static ability that reduces spell costs apply to spells cast by all players or only the controller of the effect?

Static abilities that reduce spell costs function according to their exact text. The Comprehensive Rules (CR 112.1, 604.1) state that static abilities generate continuous effects that apply while the permanent is on the battlefield, but who benefits is entirely defined by the ability's wording.

Most cost-reduction abilities say something like "Spells you cast cost {1} less" — the word "you" restricts the benefit to only the controller of the permanent with that ability (CR 109.5). An example is Goblin Warchief, which reduces the cost of Goblin spells you cast.

Other abilities are written without that restriction, applying to all players. For instance, an effect that says "Creature spells cost {1} less to cast" with no "you" qualifier benefits every player trying to cast creature spells (CR 604.1, 601.2f). Cloud Key and Semblance Anvil work this way — opponents can also exploit the discount.

Concrete example: If you control an enchantment that says "Instant spells cost {2} less to cast," and your opponent casts Lightning Bolt, they also pay {2} less (to a minimum of {0}), because the ability places no restriction on who casts the spell (CR 601.2f).

Always read the ability carefully. The presence or absence of "you" (or "your opponents" for punishment effects) is the decisive factor in determining which players receive the cost reduction.