Trizol is a brand name for guanidinium thiocyanate. It is used in the method called guanidinium thiocyanate-phenol-chloroform extraction. Guanidinium thiocyanate is a chaotropic agent used in protein degradation. More details are found in this paper: DNA, RNA, and Protein Extraction: The Past and The Present from Siun Chee Tan and Beow Chin Yiap (https://doi.org/10.1155/2009/574398).
Diethyl pyrocarbonate (DEPC) is used to treat water to inactivate RNases. This is done through covalent modification of histidine, lysine, cysteine, and tyrosine residues. If you don’t have any molecular biology grade water, you can use DEPC-treated water to resuspend the RNA pellet.
Both reagents you mentioned are used to preserve the RNA. RNA is highly susceptible to degradation by RNases. TRIzol is a chaotropic isolation reagent that denatures proteins and thus inhibits RNases, and by performing phenol-chloroform extraction, which is a part of the TRIzol protocol, separates proteins and DNA from RNA (which is in the aqueous layer), removing RNases. DEPC is an RNase inhibitor that can be used in buffers for the resuspension of RNA isolates, for supplementation of electrophoresis buffers... in order to prevent RNA degradation in the process.