  From the Sloan Digital Sky Survey (SDSS) Data Release 5 (DR5), we extract a
sample of 4594 galaxies at redshifts 0.02<z<0.03, complete down to a stellar
mass of M=10^10 Msol. We quantify their structure (Sersic index), morphology
(Sersic index + ``Bumpiness''), and local environment. We show that morphology
and structure are intrinsically different galaxy properties, and we demonstrate
that this is a physically relevant distinction by showing that these properties
depend differently on galaxy mass and environment. Structure mainly depends on
galaxy mass whereas morphology mainly depends on environment. This is driven by
variations in star formation activity, as traced by color, which only weakly
affects the structure of a galaxy but strongly affects its morphological
appearance. The implication of our results is that the existence of the
morphology-density relation is intrinsic and not just due to a combination of
more fundamental, underlying relations. Our findings have consequences for
high-redshift studies, which often use some measure of structure as a proxy for
morphology. A direct comparison with local samples selected through visually
classified morphologies may lead to biases in the inferred evolution of the
morphological mix of the galaxy population, and misinterpretations in terms of
how galaxy evolution depends on mass and environment.
