This depends 100% on the license to their intellectual property they give you. No general answer can be given. An example for someone who writes that out very clearly is Texas Instruments. Last page of any evaluation board's user guide contains a variation of a legal text containing:
These resources are intended for skilled developers designing with TI products. You are solely responsible for (1) selecting the appropriate
TI products for your application, (2) designing, validating and testing your application, and (3) ensuring your application meets applicable
standards, and any other safety, security, or other requirements. These resources are subject to change without notice. TI grants you
permission to use these resources only for development of an application that uses the TI products described in the resource. Other
reproduction and display of these resources is prohibited. No license is granted to any other TI intellectual property right or to any third
party intellectual property right. TI disclaims responsibility for, and you will fully indemnify TI and its representatives against, any claims,
damages, costs, losses, and liabilities arising out of your use of these resources.
Here, TI grants you a very limited right to use the design. For example, if it's a measurement amplifier based on a TI opamp, and you replace that opamp with a drop-in compatible one from analog devices, you lose the right to use that design. (At least according to their own legal department. Whether or not that's enforcable for simple designs is up to a judge to decide, in any jurisdiction I'm aware of.) If you use the power supply unit, which might use non-TI parts exclusively, and design a circuit based on that for anything but a TI-component-based device, you'd be in breach of the license they grant you.
Other manufacturers have different terms. This is a well-known fact, and just as with software, you will need to check individually whether you're allowed to incorporate someone else's intellectual product in yours.
When buying from any hardware vendor (like Adafruit), you procure the right to a given number of physical devices working according to a specification. You are not buying the rights to use any of their (or their supplier's) intellectual property in your own designs. Adafruit doesn't have a general license for the designs they sell, as far as I can tell, but they have a few that they explicitly call "open source hardware". That will definitely come with a specific license that allows you to use that design – but according to rules, which might, for example, mean that when you use the design in your product, your customer gets the same rights about your device, and can require information about where you had design components from or even design / production files. It, again, depends on the individual license. Other licenses are just "yeah, go wild, and have fun. We're not liable for what you do."; no general rule exists, and in practice, IP licensing is a case-by-case thing.