Both find structure in graphs, but they answer different questions.
SCC asks: "Which nodes can reach each other both ways?" You get groups of mutually reachable nodes. Use this when you need to compress a graph or find cycles.
Bridges ask: "Which edges are critical?" You get edges whose removal disconnects the graph. Use this when you need to find weaknesses in a network. SCC works on directed graphs. Bridges apply to undirected graphs. Do not confuse the two.