I am adapting to UK's arrangement of data. I would not say that our records are not precise or any less precise than the UK. However, due to our country's history and being a young one at that our organization evolved differently.
If you are searching for someone who is Catholic then you will find a good deal of info within the Catholic Church parish records. I think when our country went the way of separation of Church and State that meant that they would not rely on the Church to gather and report on the population. The UK has been around a lot longer that the USA and you perfected your means of records long before my Great Grandparents immigrated to the US in the late 1800's. In the older cities on the East Coast there are some parish records in some churches. Our government allows each state to have a certain amount of independence over how the state is run. My Grandmother born in 1909 did not have a birth certificate and the only record of her birth was in the family bible which families recorded births and deaths of the family and then handed the bible down to the eldest child of each generation to continue the keeping of the records. By the time my mother was born in 1931 there was not a real official certificate of birth but doctors were to report the birth to the courthouse. Today I live in a different state and when I was born the hospital prepared a information form to make my birth certificate and had my parents sign and the hospital may have reported the birth to the county who then issued the certificate or certified copies. Since 911 you can request a copy of a birth certificate at the county recorder's office and they will take the fee and you will then receive in the mail a certified copy of the certificate from the Department of Health. So, we are still evolving and that is for my state. I have to admit it is not all the same but there are some similarity from state to state. There are times when you go to different states to do things that it is like another country. Plus, there are 50 states all doing their own thing and that is how this country is structured.
There is the state, which is divided into counties and in some states bouroughs or parishs then there are cities. With that said there is different governmental levels for each. Easy if you live here and I am certain crazy if you live in the UK. And I grapple and have a cousin educating me and guiding me thru the confusing when I look for info in England and Scotland. I walk her thru the US stuff. Plus she is just learning Ancestry and I have used it 5+ yrs.
Keep posting questions if I can help I will or someone else will along the way.