A song is something that generally consists of a lead vocal supported by various instruments such as guitar, bass, piano, and drum set—maybe some strings and synthesizers are involved as well. This form of music typically falls into the genre of what most people would consider to be "popular" or "indie" music. For example, one of Adam's original songs, Blue Skies, has a lead vocal supported by piano and synth strings.
You often hear the terms "Music Theory" and "Composition" paired together—this is because "Composition" typically insinuates more melodic, harmonic, and rhythmic complexity. Compositions are usually written for traditional instrumental ensembles and choirs, and tend to be more classical or contemporary in style. For example, Adam's composition, A Flight of Fancy, is written for concert band.
Arranging involves taking a piece of music which already exists and turning it into something new. This can involve anything from taking an entire rock band song and reducing it into a piano solo, to rewriting a traditional classical piece by adding a jazzy melodic twist and a new harmonic structure. For example, Danger Zone (originally performed by Kenny Loggins with a rock band) was re-arranged by Adam for pep band.
Adam uses Avid's Sibelius music notation software to produce high-quality engraved sheet music.