Madmadah means taking water into the mouth, moving it around and expelling it. Istinshaq means drawing water into the nose. Merely wetting the lips is not the same as rinsing the mouth.
Both are treated as emphasized sunnahs in wudu. The legal status of rinsing mouth and nose in obligatory ghusl is a separate topic and should not be conflated with this ruling.
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Sunnahs of Wudu and Their Juristic Rulings
Madmadah means taking water into the mouth, moving it around and expelling it. Istinshaq means drawing water into the nose. Merely wetting the lips is not the same as rinsing the mouth.
Both are treated as emphasized sunnahs in wudu. The legal status of rinsing mouth and nose in obligatory ghusl is a separate topic and should not be conflated with this ruling.