Wikipedia said that:
A songwriter is an individual who writes songs and can also be called a composer.
So I assume that songwriting is similar to composition.
There is certainly some overlap, but I see these as different concepts. Many composers would not consider themselves songwriters, and many songwriters would not consider themselves composers.
These terms are not synonyms. A song implies the act of singing, therefore the person who composes songs is a songwriter. Composer is more generic, as a composer can create music featuring a whole universe of instrumental/technical/aesthetical possibilities, of which songs are just a subset.
I see a lot of confusion here at Music.SE regarding the use of the word song, as it is often used regardless of whether the musical work features singing or not.
I am myself a composer, but I very seldom compose songs. I do compose most of the time, but only a small subset of this activity can be considered songwriting.