  It has been known that neutrinos from supernova (SN) bursts can give rise to
nuclear recoil (NR) signals arising from coherent elastic neutrino-nucleus
scattering (CE$\nu$NS) interaction, a neutral current (NC) process, of the
neutrinos with xenon nuclei in future large (multi-ton scale) liquid xenon
(LXe) detectors employed for dark matter search, depending on the SN progenitor
mass and distance to the SN. In this paper, we show that the same detectors
will also be sensitive to inelastic charged current (CC) interactions of the SN
electron neutrinos ($\nu_e$CC) with the xenon nuclei. Such interactions, while
creating an electron in the final state, also leave the post-interaction target
nucleus in an excited state, the subsequent deexcitation of which produces,
among other particles, gamma rays and neutrons. The electron and deexcitation
gamma rays will give ``electron recoil" (ER) type signals, while the
deexcitation neutrons produce, through their multiple scattering on the xenon
nuclei, further xenon nuclear recoils that will also give NR signals (in
addition to those produced through the CE$\nu$NS interactions). We discuss the
observable scintillation and ionization signals associated with SN neutrino
induced CE$\nu$NS and $\nu_e$CC events in a generic LXe detector and argue that
upcoming sufficiently large LXe detectors should be able to detect both these
types of events due to neutrinos from reasonably close by SN bursts. We also
note that since the total CC induced ER and NR signals receive contributions
predominantly from $\nu_e$CC interactions while the CE$\nu$NS contribution
comes from NC interactions of {\emph all the six species of neutrinos},
identification of the $\nu_e$CC and CE$\nu$NS origin events may offer the
possibility of extracting useful information about the distribution of the
total SN explosion energy going into different neutrino flavors.
