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We study bulge formation in MW/M31-like galaxies in a $\Lambda$-cold darkmatter scenario, focusing on the origin of high- and low-Sersic index bulges.For this purpose we use TNG50, a simulation of the IllustrisTNG project thatcombines a resolution of $\sim 8 \times 10^4 M_{\odot}$ in stellar particleswith a cosmological volume 52 cMpc in extent. We parametrize bulge surfacebrightness profiles by the S\'ersic index and the bulge-to-total (B/T) ratioobtained from two-component photometric decompositions. In our sample of 287MW/M31-like simulated galaxies, $17.1\%$ of photometric bulges exhibithigh-S\'ersic indices and $82.9\%$ show low-S\'ersic indices. We study theimpact that the environment, mergers and bars have in shaping the surfacebrightness profiles. We explore two different definitions for local environmentand find no correlation between bulge properties and the environment where theyreside. Simulated galaxies with higher S\'ersic indices show, on average, ahigher fraction of ex-situ stars in their kinematically selected bulges. Forthis bulge population the last significant merger (total mass ratio $m_{\rmsat}/m_{\rm host} > 0.1$) occurs, on average, at later times. However, asubstantial fraction of low-S\'ersic index bulges also experience a latesignificant merger. We find that bars play an important role in the developmentof the different types of photometric bulges. We show that the fraction ofsimulated galaxies with strong bars is smaller for the high- than for thelow-S\'ersic index population, reaching differences of $20\%$ at $z > 1$.Simulated galaxies with high fractions of ex-situ stars in the bulge do notdevelop strong bars. Conversely, simulated galaxies with long-lived strong barshave bulges with ex-situ fractions, $f_{\rm ex-situ} < 0.2$.

High and low S\'ersic index bulges in Milky Way- and M31-like galaxies: origin and connection to the bar with TNG50