As we corresponded back and forth, and as I conducted my own research, I discovered that we indeed are second cousins. This was really exciting to my family and me because the relation to this lady is on my mother's paternal side of the family, which has been quite the mystery. My mother did not find out who her biological father was until the mid to late 90s, and come to find out, he died in 1972 when my mother was only 10 years old.
When my mother was told by her grandmother who real father was, that was indeed a shock and surprise. My mother does not have any legal documentation such as a birth certificate, court record, etc. that states who her biological father was. All we had is my grandmother's and great-grandmother's word that he was the father - until now.
When I was contacted back in November about the possible DNA match, and then confirming the match through research, it was a very exciting breakthrough. My brother and I bought a DNA test for my mother so see what her ethnicity results would be, but also to see what DNA matches would show up for her. Last night I received an email stating that her DNA results are in!
Below is a screenshot showing the top results from my mother's DNA test. As you can see, in the Parent/Child relationship section there are two results. The first result is my mother's mother. I had her take a DNA test last summer when her health was failing. I wanted to make sure she took a test before she is gone. The second result is my own DNA test.
The third result is the lady who contacted me back in November. Even though AncestryDNA is suggesting that her and my mother are second cousins, the lady and I are actually second cousins and the lady and my mother are first cousins once removed.