Each OS has a different range of app access and different ways of saving files.
On iOS, to save photos and videos received via Send Anywhere app, you have to grant Send Anywhere app access to 'Photos App' and can save photo and video files in Camera Roll of Photos app. If the received file format is not supported by iOS or the received file contains an audio codec not supported by iOS, it cannot be saved in Camera roll of Photos app and are saved in SendAnywhere folder in Files app.
This is because of the unique iOS system. To maintain strong security, iOS uses 'Sandbox' system. By default, iOS creates separate files for each app to prevent them from being shared. It is a form of security that prevents the system from being manipulated negatively by an area protected against external access. Therefore, you can only save files to folders within Send Anywhere app, and you cannot select the download folder location.
On the other hand, on Android, instead of having to grant access to each app, you have to grant Send Anywhere app access to 'internal storage' of your device, so you can save all the transferred files in the download folder location set in the internal storage.
The Gallery app is that categorize and show image and video files stored in your device's internal storage. If the file format is not supported by Android OS or the file contains an audio codec not supported by Android OS, it can't be display files in Gallery app.
When you first open Send Anywhere app on your device, you will be asked to grant access to Photos app on iOS or to internal storage on Android.