Actually it is difficult at times to differentiate between subject matter and theme of a work of art , one dissolves into the other. The only yard-stick is how one presents his case. Rand alThor shows where they mix and mingle.
However, in general, theme is the topic and a subject embodies that topic. For convenience's sake we would limit our discussion to a literary work only. Subject is what the work of art is about. So the subject matter is rather straight forward. For the theme you have to delve deep because subject matter hold the theme and is embodied in it. It may so happen that they may be same as shown by the learned critic in his comment for your example, but not always. Theme is what the author or poet wants to say or mean. In an allegory, subject matter is a means to an end (the theme).
Let us explain. The Selfish Giant by Oscar Wilde is an innocent story of a giant and children (subject matter) but at heart it is about autocracy and communism (theme)— compassion and love where God resides.
Or Frost's Stopping by Wood on A Snowy Evening. It is about poets personal experience on a snowy evening, hence its subject matter. But at heart it is about man torn between the rival claims of material world and yearning for aesthetic pursuit, hence its theme.