Important to note is that you export files for final use, not for editing. If you export a file and then open it in Photoshop you lose the link to Lightroom. Use the "Edit In" option under the Photo tab to go to Photoshop and have Lightroom retain ownership of the file. Changes made to files can then be saved and a new psd file will be added to your catalog. Also note that once a file is managed by Lightroom any changes you make to the file in Photoshop will appear in Lightroom as the image is not in Lightroom, only referenced by Lightroom. The latest version of any file is what appears even if you did not use the "Edit In" option to get the file. Lightroom is a database and simply references the file as it exists on your hard drive.
Under File you have four Export options. Ignoring the main "Export" option for a moment, Export with Previous simply remembers the settings from your last export. If repetitive exports are needed this saves you a keystroke and menu choice. Export with Preset allows you to select from Lightroom and User presets and possibly others depending on social media or other software on your computer. This just simplifies the process. The preset Burn Full-Sized JPEGS opens a dialog to set the burn speed for burning a disc.
For Email will open a dialog for you to enter the email address and subject line. Your default email program is used and a new email will open with the image as an attachment ready for you to add any text you wish. The settings you make in the regular Export dialog will be honored. This is a very simple means of sending an image as Lightroom manages the image manipulation for you. For Email (Hard Drive) exports a jpg file to your computer. The dialog lets you choose the location, but the parameters are those already set in the Lightroom Presets in the Export dialog. The default is a 640 pixel (long dimension) file unless you have changed the parameters. So, these options are shortcuts and assume you already have the presets managed in the main dialog.
Export as Catalog allows you to create a new catalog with options as to what images follow. Making a selection of files would allow you to make a new catalog with only those files which could be valuable as a means of managing file types you may want to have available as a unit.
The primary Export dialog should first be set to the desired destination at the top. This influences the parts of the dialog that are available for modification, eliminating modifications that are not appropriate, avoiding confusion. You can then set your own preset parameters in the various option areas. Note that exports to email can only be jpg files so this cannot be used to send other file formats. There are a lot of options for managing export files and this extended explanation by Adobe is worth exploring if you intend to do more than the simple export.
The easiest method for exporting files is to visit the primary Export option first and set any parameters you might want or need in the various areas. Click the Add button in the lower left to name a preset and be sure that User Presets is the destination. Then your parameters will be used when you use the Export with Preset option in the main menu. This will simplify the process for you. The primary Export area is then available if a preset isn't created or you wish to change the parameters.