Honors Pre-Calculus?

Im taking Honors Pre-Calculus as a freshman right now and if I take regular Calculus vs AP Calc A/B next year, will that have an impact on the decision of the colleges?

Yes OSU loves it when you take advantage of challenging courses offered at your high school;it shows them that you can and willingly challenge yourself. They compare you to other students at your high school. They however do not look at whether you passed the AP exam. But keep in mind that they do a holistic review in which they look at 12 different areas to determine if you are someone that would thrive at OSU.
http://undergrad.osu.edu/apply/freshmen-columbus/who-gets-in

What would your math progression be if you take honors calculus?
What about if you take calculus AB?
You need classes for sophomore, junior, and senior years.