Payoff For Collar Spread Versus Bull Spread

I am doing a CFAI Problem from “Application Of Derivatives - Omega”. I can’t write the whole problem out, but this is curious: The Profit On A Collar includes the difference between St and S0:

Profit Per Collar=St + max(0, x(put)-st) - max(0, st-x(call)) - putpremium - callpremium.

But the Bull Spread Payoff features only the options, not the difference of St-S0:

(HigherExercisePrice - LowerExercisePrice - LowerCallPremium + HigherCallPremium.

Why is this?

P.S. If you need me to write the problem out for context I can, but I was more interested in whether these two formulas are always different in this way.

A collar includes the underlying (so, long the underlying); a bull spread does not include the underlying.

Thanks JJ1337. Are there any other option “procedures” that automatically include the underlying?

Jep, like protective put, covered call, etc. See one of the last posts:

I think your collar profit equation is incorrect. Collar’s long put short call so the call premium should be added

^ several mistakes in the equations.