We present the results of Hubble Space Telescope Wide Field Planetary Camera imaging in V-606 and I-814 of five compact narrow emission Line galaxies (CNELGs) and four slightly more extended faint blue galaxies (FBGs) with 20.3 less than or equal to B less than or equal to 22.4 and redshifts z similar to 0.22-0.66. Half-light radii are measured to span from 0."14 to 0."67, thus yielding small sizes of R-e similar to 1-5 kpc (H-0 = 50 km s(-1) Mpc(-1), q(0) = 0.1). The new scale lengths, in combination with previous Keck measurements of velocity widths, continue to confirm that CNELGs, though quite luminous (M-B similar to -21), have masses comparable to dwarf galaxies (i.e., M/M-circle dot less than or similar to 10(10)). Their low mass-to-light ratios are consistent with values corresponding to very early phases of a major burst of star formation. The spatial contour maps and surface brightness profiles of CNELGs reveal the presence of high surface brightness knots surrounded by a diffuse exponential-like component and sometimes accompanied by fans and tails. Since the knots tend to also have bluer colors, they are identified as the location of the current starburst. The diffuse component is interpreted to be an older underlying population. With the current burst estimated from the rest-frame (B - V) colors and mass-to-light ratios to involve typically similar to 10% of the galaxy mass, CNELGs are predicted to fade by less than or similar to 4 mag to reach the low luminosities and surface brightnesses of bright spheroidal galaxies, such as NGC 205. These new results provide further support for our previous suggestion that these distant, low-mass, starburst galaxies may be the progenitors of today's bright spheroidals. In contrast, although the four FBGs have similar colors and mass-to-light ratios to CNELGs, they will most likely not evolve into spheroidals but will resemble small, star-forming disk galaxies.