I've looked through the forum but I have not seen an answer that wasn't contradicted somewhere else.

What is the difference (if any) between giving up parental rights and terminating parental rights?

Also, how do these things come into play if the parent who hasn't given up/terminated rights passes away?

If it helps, I live in NY state, child is an infant, there is no other adopting parent (for now).

Thanks in advance.

You can't "give up" your rights. A termination of parental rights (TPR) MUST be affirmed by a court, otherwise it never happened. You can request that a court grant a TPR, but its always the court's decision.

If a ANY parent, whether natual or adoptive passes away then they can't exercise any rights so I'm not sure I understand your question there.