Happy Birthday to you is a rhythm featuring a dotted crotchet followed by three crotchets. The Star Spangled Banner also uses this rhythm. The comparison holds up to the end of the verse.
The other examples have entirely different rhythms. America, for instance, begins with a quaver, followed by a dotted crotchet and a quaver. To compare rhythms it is easiest to see them written out on the stave. You don't need to read music to compare the appearance of the notes.
The rhythm is typically called the melodic rhythm or word rhythm found in the song. The beginning of Happy Birthday (Happy birthday to you) has the same word rhythm as Oh, say can you see.