This work reports, for the first time, the synthesis of silver nanoparticles using extracts of the species of Sargassum natans and Sargassum fluitans (AgNPs-S). Their antibacterial and catalytic properties are compared with silver nanoparticles obtained by chemical synthesis (AgNPs-C). The characterization of AgNPs-S and AgNPs-C was carried out using ultraviolet–visible spectroscopy (UV–Vis), dynamic light scattering (DLS), zeta potential, a scanning electron microscope (SEM), X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), and thermogravimetric analysis. The synthesis of silver nanoparticles using Sargassum extract was optimized through varying experimental parameters, such as the type of solvent used to prepare the extract, the volume of the extract, and the pH of the system. The most efficient sample (AgNPs-S) was prepared with a water–ethanol-based extract, using a 3:1 volumetric ratio of extract: a precursor salt with the addition of 1 mL of NaOH pH = 14. The AgNPs-C were spherical in shape, with an average particle size of 11.55 nm, while the AgNPs-S were polyhedral shaped, with an average particle size of 26.39 nm. The synthesized AgNPs-S were found to have significantly higher catalytic activity for the degradation of methylene blue and more effective antibacterial activity against Staphylococcus aureus and Pseudomonas aeruginosa than AgNPs-C.