mjhjmtu

I've copied a .gdb folder from a main folder to another and all the files that were created using ArcMap weren't there in the copied folder.

Why weren't these weren't moved as well?

Shouldn't they be there in that folder?

It sounds as if you copied the .gdb folder within Windows. Per Esri:

Note: Managing file geodatabases, including copying, renaming, and
deleting data, should always be performed with ArcGIS and not with
Windows Explorer. The tools in ArcGIS ensure that no data loss or
other problems occur.

Please copy the geodatabase (which will include all tables, feature datasets, and feature classes) using ArcCatalog. It is also possible to complete this in a script; I believe the tool there is arcpy.Copy_management

As noted by @GBG, if you copied in ArcCatalog: "After you moved the files maybe you were looking in that directory with an opened instance of ArcCatalog. Try hitting the F5 button to refresh the directory and see if your files are where you expect them to be."

What are the file you're talking about isn't totally clear but if you are talking about data resulting from an export or a geoprocessing output, then one possibility is that you don't have changed the default output (in my installation it's C:UsersusernameDocumentsArcGISDefault.gdb) you could look there if you find your file;

If you're talking about other file and you created them recently you could do the same step, when arcgis will ask you to save the file it will show you the last used location so you know where to look for your file

I would reference you to Esri's Overview of copying geodatabases page which provides:

There are a number of reasons and multiple workflows available for making copies of a geodatabase. Here are a few common cases.

Make a simple copy of a geodatabase, for example, to copy a file geodatabase.

Make a copy of a geodatabase from one type to another, for example, to copy an enterprise geodatabase to a file geodatabase.

Users need to make replica copies to use in version-based workflows and replication scenarios. For example, multiple offices in an organization may be geographically distributed, and each requires a synchronized (up-to-date) copy of the geodatabase. Perhaps each office maintains data for its geographic region and periodically shares its updates with other offices. In this case, you will use geodatabase replication. This set of capabilities provides tools for working with distributed enterprise geodatabases

To perform the copy, using the Copy tool; Copying a geodatabase using the Copy tool

The primary mechanism to copy a geodatabase using geoprocessing is the Copy tool. This tool is found in the Data Management Tools toolbox in the General toolset.

The Copy tool can be used to make a copy of an existing geodatabase of the same type (for example, to make a copy of a file geodatabase). Both the schema and all the contents of the geodatabase will be copied.

You can also use Copy to copy an individual dataset between two geodatabases of any type. For example, you can copy a feature class from an ArcSDE geodatabase to a personal geodatabase.

Copy tool parameters:

Syntax
Copy_management (in_data, out_data, data_type)
Parameter Explanation Data Type

in_data - The data to be copied.

Data Element

out_data - The location and name of the output data. The file name extension of the output data must match the extension of the input data. For example, if you are copying a file geodatabase, your output data element must have .gdb as a suffix.

Data Element
data_type - (Optional) - The type of the data on disk to be copied. This is only necessary when the input data is in a geodatabase and naming conflicts exist, for example, if the geodatabase contains a feature dataset and a feature class with the same name. In this case, the data type is used to clarify which dataset you want to copy. - String

Copying a file geodatabase in its entirety using Windows Explorer is fine to do. In this respect it is just like any other folder.

What you cannot do is copy anything within a file geodatabase using Windows Explorer.