Two different layers of the same area have to be united to form a single layer

You can try with the geoprocessing command vector > geoprocessing tools > union.

See https://grindgis.com/software/qgis/basic-editing-tools-in-qgis

For your purpose, the column with the attribute can be called 'before' in the first layer and 'after' in the second layer, or something similar. I think the result will be what you're looking for.

As mentioned above, the Union tool in QGIS will solve the problem. As per the documentation:

An Overlay layer can also be used, in which case features from each layer are split at their overlap with features from the other one, creating a layer containing all the portions from both Input and Overlay layers. The attribute table of the Union layer is filled with attribute values from the respective original layer for non-overlapping features, and attribute values from both layers for overlapping features.

The key there, being 'attribute values from both layers for overlapping features'.

once you have your overlapping features and attribute values, you can create a new calculated field, which is simply att1 - att2. this will be your 'difference' field.

You can create this field by going into your union output dataset (maybe save it as something appropriate first, shapefile/geopackage, whatever your fancy). then right click > Properties > Fields > Field Calculator (the little abacus button).