In typical seven note scales like the major scale and minor scale, the scale degrees are numbered from 1 to 7, beginning on the tonic and ending on the leading tone.
The scale degrees repeat at the octave so that each pitch class has the same number value in any register.
The degrees of the scale also correspond with musical intervals, so the two terms are often used in place of each other.
But intervals provide more information than scale degrees alone since their quality can be expressed as well. Interval qualities can be major, minor, perfect, diminished or augmented.