Difference atmosphericly corredted L1C and L2A

Hi there,
I know that the major difference between L2A and L1C data is that the former is atmoshperically corrected.
When I howeverd download L1C data from Sentinelhub using a WMS request I can also get L1C data atmospherically corrected. Simply by using custom_url_params={CustomUrlParam.ATMFILTER: ‘ATMCOR’}.

So what is then is the difference of requesting L1C data with CustomUrlParam.ATMFILTER: ‘ATMCOR’ and requesting L2A data?

ATMCOR (and similarly DOS1) is less accurate as it is based on lower scale Sen2Cor calculation on anchor tiles and then statistical comparison of the data in neighboring tiles. This does generally pretty good job in terms of basic atmospheric effects, but does not work well in the neighborhood of the clouds and is not terrain-corrected.
More info here:

We expect ESA to soon start providing L2A data on the global scale (last estimate was end of September 2018) and we will be providing these data within Sentinel Hub as well. We do however expect that archives will not be processed for quite a while, so only new data will be available in this way.

OK thank you, that helps.