Here is a page from the index for births in New Jersey from July 1, 1890 through December 31, 1900 available through the Archives. The baby's name, or "male" or "female" if unnamed, is listed first, and the father's initial is listed next. The dates have been accurate for all certificates that I have viewed. Using the birth of Robert Bosset, for example, we can see in the index that his father's first name begins with R, the date of birth was January 10, 1898, and that the certificate was filed in Newark, which is place number 36.
The birth certificate for Robert Bosset matches the information in the index and also provides the full names of both parents. You also get to see the address of the birth (likely the family's home), as well as his birth order and how many children are still living. This is very helpful information and why you should always seek out the original record.
FamilySearch and Ancestry have a record of this birth in their indexes. Their indexes provide additional information not contained in the older indexes from the Archives, such as full names of parents and their ages. BUT: the year can be off by one. The year of Robert's birth is incorrectly listed as 1897, not 1898. This is because the volume held births from July of 1897 through June of 1898. It is unfortunate that while creating these indexes, greater care was not taken to record the year of birth. The indexer needed to have viewed the actual certificate to generate the parents' names and ages for the index and, in hindsight, should have also entered the year of the event.