The present study aimed to conduct a comparative investigation of the biological properties of phenolic and polysaccharide extracts obtained using an ultrasound-assisted technique from Aloe vera gel and their effects on each stage of the wound healing process in in vitro experimental models. HPLC analysis showed that the phenolic extract contained aloin, ferulic, and caffeic acid, as well as quercetin dihydrate, as major compounds. Capillary zone electrophoresis indicated the prevalence of mannose and glucose in the polysaccharide extract. Cell culture testing revealed the anti-inflammatory properties of the phenolic extract at a concentration of 0.25 mg/mL through significant inhibition of pro-inflammatory cytokines—up to 28% TNF-α and 11% IL-8 secretion—in inflamed THP-1-derived macrophages, while a pro-inflammatory effect was observed at 0.5 mg/mL. The phenolic extract induced 18% stimulation of L929 fibroblast proliferation at a concentration of 0.5 mg/mL, enhanced the cell migration rate by 20%, and increased collagen type I synthesis by 18%. Moreover, the phenolic extract exhibited superior antioxidant properties by scavenging free DPPH (IC50 of 2.50 mg/mL) and ABTS (16.47 mM TE/g) radicals, and 46% inhibition of intracellular reactive oxygen species (ROS) production was achieved. The polysaccharide extract demonstrated a greater increase in collagen synthesis up to 25%, as well as antibacterial activity against Staphylococcus aureus with a bacteriostatic effect at 25 mg/mL and a bactericidal one at 50 mg/mL. All these findings indicate that the phenolic extract might be more beneficial in formulations intended for the initial phases of wound healing, such as inflammation and proliferation, while the polysaccharide extract could be more suitable for use during the remodeling stage. Moreover, they might be combined with other biomaterials, acting as efficient dressings with anti-inflammatory, antioxidant, and antibacterial properties for rapid recovery of chronic wounds.