Many people say "Access" when what they really mean is Jet or ACE. "Access" is the application development environment and can use ANY ODBC compliant data source. It is tightly integrated with Jet or ACE depending on the version and so the products are inseparable in the minds of many. "Access" uses Jet or ACE to store the objects you develop such as forms, reports, queries, etc. The data used by your application may also be stored using Jet or ACE. But it can also be stored using ANY ODBC compliant database engine such as SQL Server, MySQL, and Oracle.
Access(actually Jet or ACE) is not the best choice of database engine for a web application. You can do it via ODBC from ASP or any other platform that supports ODBC but performance would be better with SQL Server or MySQL. From ASP or other platforms, it doesn't matter what database engine you use as long as you get the SQL straight. So using Jet/ACE would be no different from the program's point of view than using SQL Server. But the SQL syntax will be slightly different since each RDBMS has its own syntax and although they are all close enough so that you can read them, they are not interchangeable. There is a difference with the hosting requirements. Not all services support Jet and/or ACE so you would have to find a service that supports Jet or ACE if that is what you end up using.
If you are using Access 2013, your integrated database engine is ACE but if you use Access to create a web app, Access will use SQL Server to store your data. It will NOT use ACE.
You need to be clear on where you are going with this project. Do you want an Access FE? Do you want it to be a client/server app or a web app? In any case, you almost certainly don't want an "Access" BE. All the bad things you will ever read about "Access" are written by people who are not able to distinguish Access from Jet/ACE which are completely separate products and can be installed without an Office license and do not require that "Access" be installed to run.
