Similarities: both salt marshes and mangrove swamps are areas dominated by plants and close to the coast. They both can tolerate periodic floods of salt water and are referred as coastal wetlands, being influenced by tide.
Differences: marshes are dominated by low shrubby or herbaceous vegetation, while mangroves are dominated by trees. Salt marshes can be found in colder coastlines, but mangroves don't because it suffers damage from freeze events.