Non-resonant Fe ii* (λ2365, λ2396, λ2612, λ2626) emission can potentially trace galactic winds in emission and provide useful constraints to wind models. From the 3.15′ × 3.15′ mosaic of the Hubble Ultra Deep Field (UDF) obtained with the VLT/MUSE integral field spectrograph, we identify a statistical sample of 40 Fe ii* emitters and 50 Mg ii (λλ2796,2803) emitters from a sample of 271 [O ii]λλ3726,3729 emitters with reliable redshifts from z = 0.85−1.50 down to 2 × 10-18 (3σ) ergs s-1 cm-2 (for [O ii]), covering the M⋆ range from 108−1011 M⊙. The Fe ii* and Mg ii emitters follow the galaxy main sequence, but with a clear dichotomy. Galaxies with masses below 109 M⊙ and star formation rates (SFRs) of ≲ 1 M⊙ yr-1 have Mg ii emission without accompanying Fe ii* emission, whereas galaxies with masses above 1010 M⊙ and SFRs ≳ 10 M⊙ yr-1 have Fe ii* emission without accompanying Mg ii emission. Between these two regimes, galaxies have both Mg ii and Fe ii* emission, typically with Mg ii P Cygni profiles. Indeed, the Mg ii profile shows a progression along the main sequence from pure emission to P Cygni profiles to strong absorption, due to resonant trapping. Combining the deep MUSE data with HST ancillary information, we find that galaxies with pure Mg ii emission profiles have lower SFR surface densities than those with either Mg ii P Cygni profiles or Fe ii* emission. These spectral signatures produced through continuum scattering and fluorescence, Mg ii P Cygni profiles and Fe ii* emission, are better candidates for tracing galactic outflows than pure Mg ii emission, which may originate from H ii regions. We compare the absorption and emission rest-frame equivalent widths for pairs of Fe ii transitions to predictions from outflow models and find that the observations consistently have less total re-emission than absorption, suggesting either dust extinction or non-isotropic outflow geometries.