Affinity
Affinity is a per-element measure of how attuned a character is to fire, water, air, or earth. It's an optional byproduct some abilities produce — not every ability, or even every Skill, interacts with it at all (Thieving, for instance, produces none and needs none).
The core mechanic — how affinity grows, and how it makes elemental use cheaper/stronger, including synergy between allied elements and dissonance between opposed ones — is defined on Pneuma (see Pneuma's Three Laws and its Affinity section). That page covers affinity as it applies to spellcasting and physical abilities powered by pneuma.
Scope: global per element
Affinity is tracked globally per element, not per skill. Any elementally-tagged ability, in any skill, feeds the same pool: smelting at the forge and casting fire spells both build the same Fire affinity, and both benefit from it. A blacksmith who spends years at the forge will cast a hotter fireball than one who's never touched fire, without ever having cast a spell.
This generalizes Pneuma's Law III ("affinity grows by spending that medium — casting or exertion") beyond spellcasting to any ability tagged with an element, regardless of which skill it belongs to.
Pure affinity
Alongside the four elemental tracks sits pure affinity, defined on Pneuma: the track for workings of unshaped pneuma. Physical combat abilities and untyped spells like Blink both train it and benefit from it — a warrior's Cleave and a mage's Blink feed the same pool. Pure is not a fifth element (media are matter; pure pneuma is the substance itself), and mundane abilities such as Thieving's still engage no affinity of any kind.