Confusion on default-free rates

Dear Gurus,

I have this example from CB from CFA institute.

What I am confused about is that, is there any difference between A (default-free nominal bond) and C (default-free inflation-indexed bonds)?

Regarding BEI, CB says difference between default-free zero-coupon bond nominal rate and real rate.
What Schweser says about BEI is that difference between yield on non-inflation indexed bond - yield on inflation indexed bond.

So I reorganized them, risk free nominal rate = risk free inflation indexed bonds, risk free real rate = risk free non-inflation indexed bonds. but having this example, it made me confused.

Another question, if you know. I am on a reading #46, The yield curve and the business cycle. It studies about correlation between yield and real economy. After they talk about economies and financial crisis suddenly talk about “Business cycle” I thought business cycle is something like “growth ->maturity” this cycle or “supply-demand, production related” cycles. Here what they mean about business cycle is about real economic activities. right? Economically good times and bad times.

Thanks teachers in advance for your help!

Here is the answer for the example.

The coupon rate on the nominal bond includes an inflation premium, while the coupon rate on the inflation-indexed bond does not. Therefore, the coupon rate on the inflation-indexed bond is a real rate while the coupon rate on the nominal bond is not.

Well noted! Thanks,
What you are saying is 100% correct right?
There are a lot of explanations from different sources saying different things.