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As I understand it, there is no difference.
Both global costmap and local costmap are implemented as plugins for costmap_2d::Layer. Therefore, unless the plugin intentionally changes its handling, it will be "The resolution of the map in meters/cell." as explained in the costmap_2d documentation.
The same costmap_2d documentation says the following
The following parameters can be overwritten by some layers, namely the static map layer.
I think the static map layer is usually used in global costmap. The following parameters can be overwritten by some layers, namely the static map layer. This is probably overridden by the resolution in the map topic.
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