A leaf is an organ of a vascular plant, as defined in botanical terms, and in particular in plant morphology. Foliage is a mass noun that refers to leaves as a feature of plants.
Typically a leaf is a thin, flattened organ borne above ground and specialized for photosynthesis, but many types of leaves are adapted in ways almost unrecognisable in those terms: not flat (such as many succulent leaves and conifers), not above ground (such as bulb scales), or without photosynthetic function (consider for example cataphylls, spines, and cotyledons).
Conversely, many structures of non-vascular plants, or even of some lichens, which are not plants at all, do look and function much like leaves. Furthermore, several structures found in vascular plants look like leaves but are not actually leaves; they have different structures and origins. Examples include phyllodes and phylloclades.