China's birthrate did decline with the one child policy (1979). But it declined way more in the decade prior to the introduction of the one child policy.
"晚、稀、少" : “late marriage, longer spacing, and fewer children” was a little known policy introduced in 1970 that encouraged late marriage and fewer births, and which had way bigger effects than the compulsory one child policy.
Take this as anecdotal, of course.
For certain people (mostly ethnic minorities) there was a higher limit. In rural areas, the limit was usually more relaxed than urban areas.
Many women who got pregnant before they were allowed had to have abortions. Some women were forced to have IUDs, and some women were sterilized.
So, depending on who you were, where you were, and how old you were, the one child policy might have restricted you to one child, or it didn't.
National-level, f you worked for the government (military, healthcare, PCC) you weren't allowed to have more than one child without loosing your job (if you were grunt-level) or paying and having your career path stilled (if you were CO-level).
For other workers, it was more or less a "state-level" implementation with governors deciding how to enforce the rule. In most places, farmers had the right to have two children and could ask to have one more. City workers only one and had to pay different amount depending on the city and the governor for the second. Some governors were really, really hard on enforcement (forced abortion...) while other were more lax and made people pay acceptable amount for the second child.
Still, even without hard enforcement, the illegal child have no paper, cannot join legal school and isn't present on the family register (and can't work/live anywhere legally). This is one of the 3 internal problem the Chinese government will have with the generation.
http://m.statisticstimes.com/demographics/china-vs-india-pop...
You can see that China bends the curve compared to India.
What charts?
Fertility rate: https://fred.stlouisfed.org/series/SPDYNTFRTINCHN
Birth rate: https://fred.stlouisfed.org/series/SPDYNCBRTINCHN
And it is not like the Chinese govt didn't try, they were serious about it. It's just that birth rates are mysterious. People will have kids when they want to, and will stop having kids when they want to, and they will listen to nobody. No authority.
China suppressed its birth rate with its one child policy.