My family and I are looking for a relative whose mother gave him up
for adoption at birth in the early 1950's in Modesto, California.  We
believe we know the adopted name.  We have the original birth
certificate (biological mother and father's name) with a number in the
upper-right hand corner.  Our understanding is that there would be a
second birth certificate for the adoption (adopted parents name) and
that this second "birth adoption certificate" would have the exact
same number as the first certificate.

Is this true?

We want to obtain a copy of this "adoption birth certificate" as this
would verify we do indeed have the correct name of the adopted
relative.  How can we obtain a copy of this second birth certificate?

We have obtained an address for this individual and would like to meet
him and welcome him but want to be certain before we proceed with
contact.

Also, a woman who runs her own search service said she can confirm the
name and number on the adoption birth certificate but wants $150. 
What does she have that we don't?

Thank you kindly.

Cynthia Diane