Thanks for the link. It's a bit basic, but it does have some good info: I did not know that bond indices rebalance monthly. Is there any literature to justify the indices themselves changing so often?
Well the index itself justifies them changing, right? It is an intermediate bond fund, thus it must hold substantially intermediate bonds. Note, that doesn't mean on average the maturity comes out intermediate - the individual bonds held must be intermediate term. Thus the fund can not, by definition, hold the bonds until maturity. That's why your simple equation doesn't work. And the SEC mandates that if you put the word "intermediate" in the name of the fund you must hold mostly intermediate bonds - hence active vs. passive doesn't matter. You will have a lot of turnover just on maturity alone.
Next for corporate bonds there are calls - the bonds don't even exist until maturity in many cases. They are called and you must buy new ones with the returned capital.
Finally there are *vastly* more bonds than there are equities. Constructing a index for equities is trivial compared to that for bonds, the composition changes more slowly for equities (there are a few IPOs per year and a few de-listings). Bonds are issued and disappear all the time on the other hand. The bond index updates monthly not arbitrarily but because the market is changing that fast and for the index to actually track it needs frequent updating.
In summary they are different because the bond market and equities markets are not at all similar in any way, shape or form. Bonds are issued and called far, far, far more frequently than shares of equity are.