To many, the terms composer and songwriter are interchangeable, In reality, they are not! They certainly share many common skills but there is a significant difference between the two.
A songwriter writes a single melody line and lays it over a chord progression. Lyrics are added if the song is to be a vocal tune. The order in which he or she creates these elements is irrelevant.
Sometimes these elements are created by a pair or team of writers. Sometimes they are created by a single writer.
A composer, on the other hand creates multiple streams of melody which harmonize at certain points to create harmony ie the chords.
Songwriters tend to use chord symbols in generating their songs - composers don't tend to work that way. Many songwriters start their songs with a chord progression - composers don't.
Songwriters tend to use basic harmonic rhythm and standard theme lengths and structures - again the composer does not.
Certainly writers can operate in the song field and the composer field but it does take the development of the knowledge, experience and the techniques of both fields!