What is a tuition waiver (in the US)? A tax proposal in the US is reported to make "tuition waivers that many graduate students receive when they work as teaching assistants or researchers" taxable.

I am currently a PhD student at a US institution.  All regularly enrolled PhD students at my institution have tuition 100% covered, whether through an external grant working for an advisor as an RA, as a TA, or through a university or external fellowship.  Tuition is not formally waived; money is actually moving between accounts, even if (in the case of TA's and university fellows) the money is moving from one university account to another.  There is a paper record as a part of my paycheck (I also get a stipend) that shows the tuition support that is being paid out.  Currently no student, to my knowledge, pays taxes on the tuition support that is paid on their behalf.

I am wondering, in the context of the proposed legislation, what are the "tuition waivers" that would be taxed?  Is it all tuition money paid on a student's behalf, as I've described above, or is it some subset of that, or is it something else?
A tuition waiver is when no tuition charges are paid at all. For instance, at my university, graduate students on research or teaching assistantships are not charged any tuition, nor are their advisors. In this sense, they have been granted a waiver for their tuition.

Note that even partial-year tuition waivers can be significant. For instance, during the 2017-2018 year, MIT would charge over $16,000 for summer tuition for graduate students, unless they're only enrolled in research!

I have yet to see any commentary on the issue of advisor-paid or department-paid tuition counts as a "tuition waiver."