We have measured the radial profiles of isophotal ellipticity (epsilon) and disky/boxy parameter A(4) out to radii of about three times the semimajor axes for similar to 4600 star-forming galaxies (SFGs) between redshift 0.5 and 1.8 in the CANDELS/GOODS-S and UDS fields. Based on the average size-mass relation in each redshift bin, we divide our galaxies at a given mass into Small SFGs (SSFGs; smaller than the average) and Large SFGs (LSFGs; larger than the average). We show that, at low masses (M-* < 10(10)M(circle dot)), the SSFGs generally have nearly flat epsilon and A(4) profiles in both edge-on and face-on views, especially at z > 1. Moreover, the median A(4) values at all radii are almost zero. In contrast, the highly inclined low-mass LSFGs in the same mass-redshift bins generally have monotonically increasing epsilon profiles with radius and disky feature dominated in the intermediate regions. These findings imply that at these redshifts, the low-mass SSFGs are not disk-like, whereas the low-mass LSFGs likely harbour disk-like components flattened by significant rotations. At high masses (M-* > 10(10)M(circle dot)), both highly inclined SSFGs and LSFGs generally exhibit distinct trends in both epsilon and A(4) profiles, which increase at lower radii, reach maxima, then decrease at larger radii. Such the feature is more prevalent for more massive (M-* > 10(10.5)M(circle dot)) galaxies or at lower redshifts (z < 1.4). This feature can be simply explained if galaxies possess all three components: central bulges, disks in the intermediate regions, and halo-like stellar components in the outskirts.