No. They certainly have partnerships on specific models (Subaru BRZ / Scion FR-S / Toyota 86, Subaru Solterra EV / Toyota bZ4X), but they are not exclusive, and each have their own platforms and powertrains for most of their models.
Toyota has partnered with Mazda as well - for example, there was Mazda 2 rebadged as a Toyota Yaris for a few years.