You expect that any material in public libraries is available to you. There may be a few exceptions, such as adult material not being accessible to minors, or some very rare or delicate materials that need to be handled with special care and cannot be checked out. Nowadays when you do an Internet search you expect to access any web site for the same cost and at the same speed.
There is free access to the Internet at many locations, from public libraries to places such as malls, coffee shops, and the like. The connections at these places are usually not that fast, and you are sometimes forced to provide personal information in exchange for the access. If you want an Internet connection at your home or business you have to pay for it. Your search choices are the same regardless of your Internet Service Provider.