You can store data in any file. You can make a spreadsheet a data file that contains the same information as a database, you can even import spreadsheets into a database because they are so similar. The issue that arises is that the data file becomes locked to one user and then requires that user to be out for another to be able to enter data. Databases allow for a central depository for users to collaborate and share information. They can access information in real time after another user has entered it. If I enter a piece of information another user can search for it and see the information I entered. You can not do that with a flat file without a database hook behind it like SharePoint or Google docs, nor can you do it by itself.
But I digress, a database is an area where multiple users can input information into at the same time. That is the fundamental explanation of what a database is...any database. Otherwise it would just be a file. Do you ever wonder why a access database file ends with mdb and a sql database file also had the same extension of mdb, why do you think that is? You studied this and have far more school book knowledge than I do, enlighten me..
No, that is not the correct fundamental explanation of what a database is.
Okay firstly, to what do you refer by "sql database file"? Do you refer to a database file created specifically by MS SQL Server, or do you instead refer to a database file created by any SQL type DBMS software package? Whether MS SQL Server uses the *.mdb (presumably short for "Microsoft Database") file extension, I cannot presently confirm (I don't have a copy installed, and I can't be bothered to try and research it). As to why they might have chosen it if they did, maybe because it's simple and has an 'm' for Microsoft? If you're under the mistaken belief that all SQL based DBMSs use the *.mdb extension, I can categorically state that this is not true; I have a database in a MySQL installation right here which actually uses *.frm and *.ibd files for instance. Furthermore *.mdb is not the only file extension used by MS Access, it is one of many (see here). *mdb is simply the file extension used by MS Access 2003 and below for the most common file type, replaced by *.accdb in version 2007 onwards where new file formats were introduced.
Let's recognise that sometimes words are misused, just as people may call any tablet computer an "iPad", or a vacuum cleaner a "hoover", the term "database" is commonly and incorrectly used instead of DBMS or perhaps simply "database system", even by myself at times. I'm trying to be accurate here in distinguishing between a database and a DBMS / database system. A database is a collection of data. A DBMS (database management system) / database system is a software package providing an interface (including "management" functionality) to a database. A "flat file" can indeed be considered a database (see here). A spreadsheet could technically be labelled as a database. A set of simple files in a folder may perhaps be considered a database. The database files created by a DBMS are in essence just flat files - files containing related data with a specific structure.
Here are a few references from books I have here on my book shelves:
"Understanding Computer Science, for advanced level" by Ray Bradley, page 562:
The modern database
Put simply, a database is a collection of interrelated data - rarely (perhaps on a simple micro system) containing just a single file, but more often containing a collection of several or even many files. If a database can work only on one file at a time, then it is called a flat-file database. In addition to these basic files which can be modelled in a variety of ways, there would be some program or a set of programs to carry out operations such as data entry, and generate queries which can extract a variety of information specified by the users of the system. At the most basic level, an 'address book', or even a 'list containing telephone numbers' could be regarded as examples of very simple databases. However, in this particular chapter, we will take a general look at the DataBase Management Systems (DBMS)...
When databases are undertaken within the DBMS environment, computerisation should ensure that the database is much more convenient to operate. The DBMS should also ensure that it's more efficient to enter and extract the data...
"The essence of Databases" by F.D.Rolland, page 1 (not the most clear of texts, but recommended reading):
1.1 What is a database system?
A database system is any computer-based information system where the data that supports that system may be shared. By 'shared', we mean that the data can be used by a wide variety of applications and is not arranged in such a way that it can only support one particular application.
1.2 Database systems and file processing systems
Computers store data in files. A file is a collection of records on a common theme. For instance, we can have a stock file consisting of stock records, a customer file consisting of customer records and so on. Each record consists of data that is subdivided into fields. For instance, we could have a book file consisting of book records, with each book record having fields for ISBN number, title, and author. In a traditional file processing system, specific sets of files are created and manipulated by specific applications. A database system is different. With a database system, files are not tied to and maintained by specific applications. Instead, they are integrated in such a way that the data within them may be shared by an indeterminate set of applications.
Same book, page 4:
A fundamental characteristic that distinguishes a database system from a traditional file processing system is that a database system allows many different uses to be made of the same data. The use of the data is not tied to or controlled by any single application. Instead, it is shared amongst different applications. This is achieved by removing the responsibility for creating and maintaining the stored data away from the individual applications and passing this to an underlying layer of software known as a 'database management system' (DBMS). The DBMS acts as a controlling layer between the users of the applications and the data itself.
Note that in the latter two references the author is describing a database SYSTEM (DBMS), not simply a database!
So as you can see, no mention whatsoever of multiple users in any sense. Let's consider a simple hypothetical example where we have a data file which two applications wish to modify. To write to the file, they have to obtain write access via the OS. Only one application can get write access at any time. This is the common/fundamental multi-access problem you described. A simple flat file database (which can truly be considered a database as shown with the above references), still has this exact same problem. A modern DBMS however will typically have been built to provide a solution to this problem. The file access is done only by the DBMS application, and the interface provided by the DBMS to applications provides a means for simultaneous read/write access. For reliability, the DBMS will typically be built to be ACID compliant, including features suck as locks and transactions.
While multi-user/application access (simultaneous or otherwise) is a fundamental feature of a DBMS and a major objective behind there creation (to combat data duplication present in using completely independent applications), it is not a fundamental component of any and all databases, by the correct definition of a database.
I can also feel the urge to be pedantic about your use of the term "real time", but I'll resist it, it's not important.