Sites should always have a “Terms of Service” (TOS) or “Licensing” or similar section that needs to be read carefully. Did we just say that?
Unless images are in the Public Domain (more on this below) then they are licensed to the user in some way, with an agreement governing that license. When you buy a stock photo, you are granted a similar license, you don’t own the image. You cannot claim it as your own and resell it – this is generally true for free stock photography as well. This of is as purchasing the photo for $0.00. Free photos and free textures are often licensed under the Creative Commons license, or a traditional copyright outlined in the site TOS. There are many flavors of both these methods and they grant varying uses.