[Abridged] We study the spectral properties of intermediate mass galaxies as a function of colour and morphology. We use Galaxy Zoo to define three morphological classes of galaxies, namely early-types (ellipticals), late-type (disk-dominated) face-on spirals and early-type (bulge-dominated) face-on spirals. We classify these galaxies as blue or red according to their SDSS g-r colour and use the spectral fitting code VESPA to calculate time-resolved star-formation histories, metallicity and total starlight dust extinction from their SDSS fibre spectra. We find that red late-type spirals show less star-formation in the last 500 Myr than blue late-type spirals by up to a factor of three, but share similar star-formation histories at earlier times. This decline in recent star-formation explains their redder colour: their chemical and dust content are the same. We postulate that red late-type spirals are recent descendants of blue late-type spirals, with their star-formation curtailed in the last 500 Myrs. The red late-type spirals are however still forming stars approximately 17 times faster than red ellipticals over the same period. Red early-type spirals lie between red late-type spirals and red ellipticals in terms of recent-to-intermediate star-formation and dust content. Therefore, it is plausible that these galaxies represent an evolutionary link between these two populations. They are more likely to evolve directly into red ellipticals than red late-type spirals. Blue ellipticals show similar star-formation histories as blue spirals (regardless of type), except they have formed less stars in the last 100 Myrs. However, blue ellipticals have different dust content, which peaks at lower extinction values than all spiral galaxies.
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