Go44Dad does a good job of outlining the different sources of funding.
What you need to do is to normalize all offers to dollar values against cost of attendance for the schools as a means of "comparing" for yourself.
When son received offers, there was no standard that every school used. Some would talk percent, others would talk about line items (i.e., we'll cover room, tuition & books, or we'll cover everything except fees, etc). Some would simply offer a $ total.
The first thing I would do is break all of it down to actual dollar values, so actual dollar value or tuition, etc., etc.. Then I could determine what the total dollar value of the scholarship offer was (which is all that really matters), and then could compare that to the cost of attendance to determine what my out of pocket would be (again, all that really matters). Most of the info you need for schools is available online (cost of tuition, fees, books, boarding, meal plans, etc.)
This factors in out of state, other monetary resources (academic or needs based), etc.
Then and only then can you have a real understanding of the offers, how it impacts your financial well being and your ability to cover your end.
And to your question of "70% of what, 40% of what?", you need to ask the coach offering. You can't assume that what Coach A says will mean the same thing as Coach B. One may be referring to Cost of Attendance and the other may be referring to just tuition. Only way to know is to ask THAT coach.