Perfect pitch, in non-technical terms, is the ability to name a pitch without any previous references.
For example, if someone plays a C# on a piano, someone with perfect pitch can tell that it is a C# without hearing or knowing what any other note was or looking at the keyboard. It is solely based off of sound.
Relative pitch (also in simple terms) is something that is more of a skill that one picks up after hearing many intervals. It’s the similar to perfect pitch except I need a reference point. Once someone plays a note an tells me what it is, I can tell them what any note is by using intervals.
For example, someone plays a C# and tells me it is a C#. Then, they play an E. I can tell them that is an E because I know that the difference between the first note and the second note is a minor-third.
Sometimes I wonder if perfect pitch can also be an acquired skill…
I don’t know what the term is for your daughter’s ability to match the notes, but it is definitely a talent. I know someone with a really good voice who, when singing with a piano, has a very hard time matching the pitch of the piano. She’ll just keep singing and not realize she is a few intervals off from the piano’s key.