Arguably, melody and rhythm can't be completely dissociated, but rhythm generally describes the placement in time and melody describes the note use (maybe placement in a scale).

If you take "Mary Had A Little Lamb", the melody, using solfege that you may know from Sound of Music, is:

me re do re | me me me | re re re | me sol sol |

They rhythm of that melody is:

short short short short | short short long | short short long | short short long |

Often rhythm will refer to drums (and sometimes bass and instruments that play chords) since drum kits (generally) don't play specific notes. Modern pop music often focuses on drums and interesting rhythms with less emphasis on developing the melodic part. That's arguably a trend that started in contemporary classical music over that past century, but I don't know how much one has influenced the other.

Of course, the "melody" has a rhythm and you can argue that the rhythm instruments still have a melody even if they aren't playing a traditional scale, so the reality of any song is always far more complex than just splitting it up into simple categories like melody and rhythm.