We probe the column densities and masses traced by the ionized and neutral atomic carbon with spectrally resolved maps, and compare them to the diffuse and dense molecular gas traced by [C I] and low-$J$ CO lines toward the star-forming region M17SW. We mapped a 4.1pc x 4.7pc region in the [C I] 609 m$mu$ line using the APEX telescope, as well as the CO isotopologues with the IRAM 30m telescope. We analyze the data based on velocity channel maps that are 1 km/s wide. We correlate their spatial distribution with that of the [C II] map obtained with SOFIA/GREAT. Optically thin approximations were used to estimate the column densities of [C I] and [C II] in each velocity channel. The spatial distribution of the [C I] and all CO isotopologues emission was found to be associated with that of [C II] in about 20%-80% of the mapped region, with the high correlation found in the central (15-23 km/s ) velocity channels. The excitation temperature of [C I] ranges between 40 K and 100 K in the inner molecular region of M17 SW. Column densities in 1 km/s channels between ~10$^{15}$ and ~10$^{17}$ cm$^{-2}$ were found for [C I]. Just ~20% of the velocity range (~40 km/s) that the [C II] line spans is associated with the star-forming material traced by [C I] and CO. The total gas mass estimated from the [C II] emission gives a lower limit of ~4.4x10$^3$ $M_{odot}$. At least 64% of this mass is not associated with the star-forming material in M17SW. We also found that about 36%, 17%, and 47% of the [C II] emission is associated with the HII, HI, and H_2 regimes, respectively. Comparisons with the H41$alpha$ line shows an ionization region mixed with the neutral and part of the molecular gas, in agreement with the clumped structure and dynamical processes at play in M17SW. These results are also relevant to extra-galactic studies in which [C II] is often used as a tracer of star-forming material.
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