Do colleges favor BC kids over AB? I’m in the situation where I can either take AB at school and BC online but if they don’t really distinguish the two then I won’t stress out over it.
Except for tippy top STEM schools, no.
Yes. BC covers more of the basic college level calculus.
Confused now lol
Calc AB covers the first half of Calc BC. Some schools do not even offer Calc AB while some others divide the Calc BC into 2 years with AB in the first year. Most schools cover the whole Calc BC curriculum in one year.
I’m not really talking about credit but rather rigor.
I understood your question the 1st time 
Although you could have made the title more clear to avoid confusion.
If your school does not offer BC, there is no expectation that a college will make you seek out opportunities that your HS does not provide. If you want to challenge yourself with additional calc topics, by all means do the online route. But do not do it solely for college applications.
The above only holds true, however, if your GC will mark your schedule with AB as “most rigorous” on the Secondary School Report. Additionally, if other students at your school are applying to the same colleges as you, and they have BC, that might be a consideration.
Bottom line, BC is definitely more rigorous, but that does not necessarily mean that it is necessary for you to take it.
If, after completion of precalculus, you are offered a choice of AB or BC as regular courses, then BC will appear more rigorous than AB. Whether it makes a significant difference depends on the college and your intended major (math-heavy or not).
All things being equal, BC is more rigorous than AB.
All things are not, however, equal in your case. I would not recommend taking BC online unless you aced precalc with hardly any effort at all and/or you already have a track record of doing very well in online classes.
Online is harder. You have to be much more self-motivated and when you have difficulties that aren’t easy to articulate, the instructor can’t as easily pick up on what you need from contextual clues, and for many other reasons. Calculus is hard. I would be very wary of taking it online.
Since your school only offers AB in-house, you should have no problem getting the “most rigorous” box checked off with it.
I read that Calc BC is highly regarded by top schools (like Dartmouth) because it is one of the hardest exams you can take in HS.
What @skieurope said in post #6.
I suppose it depends on the college and the overall application of the student. My D took AB instead of BC and was accepted to 4 out of 5 selective non-Ivy schools. She was waitlisted at Vanderbilt. She did not apply to an Ivy.
BC is a better course and you will learn a lot more. Nearly every (marketable) discipline requires math skills and it will probably help you in college too. C will cover series as well as take a more rigorous look at derivatives/integrals. That being said, make sure the online course is legit. Generally, you will learn better in a traditional classroom setting.
@cmsjmt Calc BC is one of the easiest AP exams in high school. Approximately half the people taking it nationwide get a 5.
@puzzled123 Higher percentage of 5 does not mean it is the easiest. Students are self selected. AP Chinese has the highest percentage of 5 and I am sure a regular student would not call it easy. Same thing for Math 1 vs Math 2 in SAT2. Math2 has a much higher percentage of score 800, but the same student may get lower score in Math 2 than in Math 1.
@puzzled123 Correlation does not imply causation. Half the people taking BC get 5’s because the students who take BC are a very self-selecting group, not because the exam is easy.
Thats true, it is self selected, but out of the 12 AP tests I have taken, it was still the easiest 5. The curve is insanely high for a math test (which has extremely objective grading). You only need around a 60% for a 5! The consensus among my high school is that its one of the easiest AP exams, where 103 out of 118 students taking it got a 5. Obviously, take this with a grain of salt, as this is only one high school (although we aren’t a highly ranked feeder school nor do we have a stellar math department).
And a lot of these same BC students who are taking AP Chem/Bio/Physics, AP Lit, or APUSH scored a lot worse on them.