We explore the gas-to-dust mass ratio (M gas /M d ) and the CO luminosityto-M gas conversion factor (α CO ) of two well studied galaxies in the GOODS-N field, that are expected to have different star forming modes, the starburst GN20 at z = 4.05 and the normal star-forming galaxy BzK-21000 at z = 1.52. Detailed sampling is available for their Rayleigh-Jeans emission via ground based mm interferometry (1.1 − 6.6 mm) along with Herschel PACS and SPIRE data that probe the peak of their infrared emission. Using the physically motivated Draine & Li (2007) models, as well as a modified black body function, we measure the dust mass (M dust ) of the sources and find (2.0 +0.7 −0.6 × 10 9 ) M ⊙ for GN20 and (8.6 +0.6 −0.9 × 10 8 ) M ⊙ for BzK-21000. The addition of mm data reduces the uncertainties of the derived M dust by a factor of ∼ 2, allowing the use of the local M gas /M d vs metallicity relation to place constraints on the α CO values of the -2two sources. For GN20 we derive a conversion factor of α CO < 1.0 M ⊙ pc −2 (K km s −1 ) −1 , consistent with that of local ULIRGs, while for BzK-21000 we find a considerably higher value, α CO ∼ 4.0 M ⊙ pc −2 (K km s −1 ) −1 , in agreement with an independent kinematic derivation reported previously. The implied star formation efficiency is ∼ 25 L ⊙ /M ⊙ for BzK-21000, a factor of ∼ 5 − 10 lower than that of GN20. The findings for these two sources support the existence of different disk-like and starburst star-formation modes in distant galaxies, although a larger sample is required to draw statistically robust results.