Stork Drop, Gotcha Day, and Birth Parent Erasure

Hi all, I am a birth mother trying to gain some insight from those who have adopted. Every so often I hear of a family celebrating 'gotcha day', the day their child's adoption was finalized. I also hear the term 'stork drop', which I am unsure the meaning of. I assume it means matching with a baby that has already been born. I really struggle with terms like this. "Gotcha", to me, seems like a child is a possession to be won. I am not an adoptee, but I would imagine that could potentially be hurtful. My birth child was not 'gotten' from me- she was given, placed from loving arms to loving arms. And I am not a stork, I am a human being who sacrificed her heart for her sweet baby who needed more than I could provide at the time. I am sure that adoptive couples don't mean to be hurtful or erase birth parents from the picture, I am sure these phrases are simply meant to be cute. But it does hurt sometimes. I feel that these phrases sugarcoat the fact that adoption is trauma to both the adoptee and the birth parents. Don't get me wrong- I love adoption and have no ill will toward those who adopt. I would just like to understand a little bit more about these terms and why they are so frequently used. Can anyone shed a little light on this for me?