If we know that label A has the same meaning as label B, we might expect the same behaviors to result from seeing either label. However, I do not think that that is always the case.
For example, in public spaces it is common to see a bin labeled ‘recycle’ next to a bin labeled ‘garbage’ (or ‘trash’). We know that items in the garbage bin will end up in a landfill. So, it shouldn’t matter if the bin is labeled ‘trash,’ ‘garbage’ or ‘landfill.’ However, when I came across a bin labeled ‘landfill’ today, I felt guiltier putting trash in there. Even though we know that garbage=landfill, labeling it landfill might make us more likely to picture a landfill and feel guilty (and possibly lead to a change in behavior).