If you do a share to Apple Devices it by default puts it into your iTunes library and there is no next button. If you’d like to save it somewhere else, in the share dialog, under settings, you’ll have to choose “When Done: Do Nothing.” That will change the share button to a next button. Then pressing next will give you the choice of where you want to save it.
Most of us are probably using compressor presets which can be added to the share menu. I have quite a few as I figure out just what a client likes/wants/works for them. I also have quick decent quality very fast settings for client approvals.