One definition of a "true" martial art is that it includes a process of evolution or maturation for the practitioner that is usually "spiritually" guided.
A self defense system could be defined as a pragmatic, no-frills this-for-that response program with no interests beyond being the last one standing.
It seems to me the former always originates as the latter.
Some problems with these definitions include who is defining "spiritual" and what that word means in that case. Another is that some enter into practice of "true" martial arts with no desire to partake of the "spiritual". So I suppose it all boils down to what YOU think it is.
I know, that didn't help.