Yes, both piano music and recorder music are written with the same kind of music notation, using the same kinds of symbols. The pitch "A" on the piano and the same pitch "A" on the recorder are written with the same musical note in sheet music.
I do not know, but I suspect that the problem your daughter is encountering is of a different nature:
On the piano, the keys are laid out in a numerical order that corresponds to the pitches. It's easy to see how one note follows the next, and where to put your fingers to find the next note.
On the recorder, however, producing different notes requires a different arrangement of the fingers on the instrument that does not line up in a nice linear arrangement like you find on the piano keyboard.
I suspect your daughter (and she's only 7, so this is a difficult task for her) finds it easy to correlate the position of a note on the musical staff with the correct key on the piano. However, she finds it difficult to correlate the position of the fingering necessary to produce a note on the recorder with the position of the same note on the sheet music. So she needs the extra help of having the name of the note written in to kind of "jog her memory" to associate the name of the note with the fingering.
None of this should be a problem. As she continues to practice the recorder, these things will become second nature and she will gradually become more able to do the mental work and the fingering work in real time as she plays the recorder and reads the sheet music.