The protocol, spec (MSC3401) and underlying client heavy lifting (matrix-js-sdk) are all Matrix; contributed by a mix of Element employees (Robert, me, Dave) and community contribs (Simon B). The app skin itself on top is Element, given most of the work and the original idea is from Element folks - same reason that Element itself is a product from Element-the-company even though 95% of the code is underlying Matrix projects. The Matrix Foundation itself is a non-profit to look after all the Matrix protocol and reference implementations but doesn’t ship user-facing products, just as W3C and Linux Foundation don’t.