This answer will focus on convoys in the Atlantic in both wars - the Japanese experience in the Pacific in WW2 diverged significantly. While convoys in both WW1 and WW2 appear similar, with destroyers and smaller ships escorting a large amount of merchant ships, they protected their charges in very different ways. In the First World War, the ability to reliably detect and sink submerged submarines was lacking. This meant that convoys could not effectively kill submarines threatening them. Instead, convoys protected shipping in three main ways. Firstly, they reduced the chance that ships would encounter a submarine. Convoys and independently sailing ships were as easy to spot for a submarine, but an individual sub was much less likely to encounter a convoy, simply because there were much fewer convoys. Convoy escorts could also interfere with a submarine's ability to approach a convoy, especially once the RN began to escort convoys with blimps or kite balloons. By spotting a submarine on approach, they could force it to submerge, greatly decreasing its speed, and allowing the convoy to escape. Finally, outlying escorts attacked submarines, with the aim of forcing them to break off their attack on the convoy. The primary aim was not to kill the submarines, but to damage and deter it.

In the Second World War, things changed significantly. The advent of sonar meant that submarines could reliably be detected. The threat environment also changed. Instead of having to protect against single submarines, wolf-packs of multiple submarines were the main threat to the convoy. This meant that submarines could no longer be driven off - if the escort devoted its attention to driving off a single submarine, as it did in WW1, then the rest of the wolf-pack would savage the convoy. Instead, submarines had to be destroyed. Convoys moved from being primarily about passively protecting shipping to actively being a killing ground for U-boats. Convoy escorts were greatly strengthened, and given better tools and training for killing U-boats. In the First World War, the majority of U-boats were sunk by mines or by hunting destroyers., with only a small proportion being sunk by convoy escorts. In the Second, convoy escorts and aircraft were the two biggest killers of U-boats.

Convoy alone could not reliably protect shipping against surface attacks. In 1917, a British convoy to Norway was completely destroyed by two German cruisers. Several convoys were destroyed or attacked by German surface raiders in WW2, including HX 84 and SLS 64. To protect against this, the escort could be strengthened with battleships - HMS Ramillies deterred an attack on HX 106 by Scharnhorst and Gneisenau in February 1941. The convoy could also have a strong protective covering force, which could speed to the rescue of the convoy, but remain separate and comparatively safe from submarine attack. This was commonly done in the Arctic theatre, and for important convoys like Operation Pedestal in the Mediterranean.