This is the difference between the yield to maturity of the bond and LIBOR
This is the spread over LIBOR that the fixed rate (bond coupon payer) receives
This spread can be split into two components:
The first is the difference between the bond coupon and the par swap rate.
(the total present value of the cash flows that results from the difference of the bond coupon and the par swap rate, paid at the fixed leg frequency)
The second is the difference between the bond price and its par value.
You can easily back out the corresponding spread over the floating discount factor curve.
Uses the Zero Coupon Yield curve

By combining the two you can change the coupon payments to either fixed or floating.
This is the yield of the bond minus the swap rate for the corresponding maturity swap

A fixed-rate bond will be combined with an interest rate swap in which the bond holder pays a fixed coupon and receives a floating coupon.
the other 3 methods all incorporate the term structure of interest rates when evaluating (ie discounting using the yields of different maturities)
This floating coupon will be spread over LIBOR and it is this spread that is the asset swap spread.
This spread is a function of the credit risk over and above the interbank credit risk.
Asset swaps can be transacted at either par or market value but usually par.
This means the asset swap is made up of the difference between the bonds market price and par as well as the difference between the coupon and the swap fixed rate.

The asset swap spread converts a risky yield into a LIBOR plus a credit spread using an interest rate swap.

One approach to calculating the asset swap is to use the bonds YTM in the calculation although this contains implicit assumptions
This spread is the difference between the yield of a bond and the yield of a government/risk free bond.
This spread is a way of comparing 2 bonds that are identical except for their quality rating.
The 2 bonds must have the same maturity date.
This spread reflects the additional yield that an investor can earn from a bond that has some credit risk relative to a government bond which has no credit risk.
The yield spread of X over Y is the percentage return on investment from X minus the percentage return on investment from Y.

Asset swaps use zero coupon swap rate
The zero-coupon curve is used in the asset swap valuation.
Asset swap spreads represent the difference between swap rates and treasury bond yields.

The asset swap spread is the spread that equates the difference between the present value of the bonds cash flows, calculated using the swap zero rates and the market price of the bond.
This spread is a function of the bonds market price and yield, its cash flows and the implied zero-coupon interest rates (Bloomberg refers this spread as the Gross Spread).

This is the rate relative to a floating index such as LIBOR that would be obtained if a fixed rate bond was converted to a floating rate asset.