As stated in this post about the internet tax, the law prohibits state and local government from taxing internet access. It doesn’t address charging sales tax on the internet sales. States that already had Internet access taxes before the ban are Hawaii, New Hampshire, New Mexico, North Dakota, Ohio, South Dakota, Texas, Washington and Wisconsin (according to the National Conference of State Legislatures.)
The bill did include a small change, leaving options for providers to tax “home page electronic mail and instant messaging (including voice–and video–capable electronic mail and instant messaging), video clips, and personal electronic storage capacity, that are provided independently or not packaged with Internet access.” That infers they’d like the option to tax other services, but not individual emails sent or instant messaging. In general Republicans wanted a permanent moratorium and Democrats wanted to keep options open for the future but both parties are in strong favor of a ban – it’s just the length or permanency that’s debated.