I have purchased many certificates over the years.
This is sometimes the only way for me to confirm relationships, but it can become costly. So I am always delighted and grateful when I receive copies form other people.
Birth certificates confirm parentage and will often list fathers occupation. They will also provide the mothers maiden name and any other surnames she may have owned. These are usually listed as formerly xxxx and late xxxx. The most commonly used term for an illegitimate child is bastard, However there are many other English words and phrases used in the records: base; baseborn; begotten in fornication; by-blow; child of shame; lovechild; merrybegot; misbegotten; whoreson. In Latin there are filius nullius (son of none - the girl did not know or want to say); filius populi (son of the people - anyone's guess); filius meretricis (son of a prostitute); filius populi means illegitimate daughter
Marriage certificates provide evidence of both fathers and their occupations. Address and occupation of bride and groom. Sometimes their ages appear although this may be described as "full age" or "over 21", Witnesses names may also help in identifying relationships. It is interesting to reflect on the evidence of whether they were married after banns, licence or certificate, this may well give rise to further ideas.
Death certificates provide the age of the deceased. Sometimes if a woman the certificate will state whether she was the wife or widow of..... The name and address of the person informing the authorities may be a relation and could be helpful. If the death was followed by a postmortem or coroners hearing this will also be recorded as will the cause of death.
Some births especially in the early years of civil registration were not registered. Not everyone was honest on certificates, this maybe because they truly did not know the birth correct name or age when registering a death. Ages on marriage certificates are notoriously incorrect for many reasons and the use of "full age" or "over 21" could hide a multitude of reasons and stop the need of parents permission. Occupations were often inflated on birth and marriage certificates, for example an "Ag lab" could become a farmer.
I have found birth certificates where when the father registered the birth he called himself one name, but when the wife did the same she referred to him under a different name. Definitely same couple.
One birth certificate I have of a lad whose siblings were adopted shortly after his birth gave me a clue. His grandmother registered his birth, his mother died shortly after his birth and clearly Dad could not cope with all the children, so the older ones were kept together and adopted by an older couple. I knew I had the correct relationships as on one certificate I had mother, father, son and grandmother. Quite a find.