They are definitely related and involve a lot of the same thought processes, but they are not the same thing. Arranging is taking a preexisting work and fitting it to a different set of instruments. Composing is writing something with enough originality to be its own piece. In effect, I tend to think of arranging as "composing from a reference point" because of how the same processes are used in both arranging and composing. Now, this can be blurred sometimes, as sometimes an arrangement of a preexisting work becomes part of a separate piece or its own piece entirely. Take for example, these 2 pieces by Beethoven, the Septet in Eb Op. 20 and the Trio in Eb Op. 38.
The trio is an arrangement of the septet, and yet is considered a separate piece from the septet. And both of them have material in the third movement that was used previously in his Piano Sonata no. 20 in G major, which is just one of many examples of Beethoven recycling his own material.
This is just one example of composition and arrangement being blurred and there are some less clear examples out there than these 2 Beethoven pieces, but as I'm most familiar with Beethoven, I chose the septet and trio as my example of the blur between composition and arrangement.
As I'm experienced in arranging pieces for a variety of ensembles and by a variety of composers, I can say for sure that there are composers that fit perfectly or almost perfectly into a note for note reduction arrangement a lot of the time such as Haydn and Mozart. And there are others for which I almost always need to subtract a little and sometimes a lot to make the reduction feasible for the players, such as Beethoven. For expansion arrangements, Beethoven is still tricky and I still sometimes have to subtract, though not as often as with reduction arrangements. However, for Haydn and Mozart, I often have to add rather than subtract if I'm doing an expansion arrangement such as solo piano to string quartet or string quartet to orchestra. This could be as simple as doublings or as complex as an added countermelody. Indeed, even in reductions, I sometimes have to add to what Mozart wrote, usually by adding tremolos or Alberti Bass where there are long notes in the original score.