How can I move pictures from my Galaxy Tab to a Samsung Galaxy S4?
You can also connect both the devices to PC and can transfer pictures from tablet to S4 by simple copy pasting.
Or plain old simple Bluetooth.
You could use FTP through Wi-Fi using an FTP client such as Wi-Fi File Explorer, ES File Explorer, File Expert, etc. for direct transfers wirelessly. Each of these apps, and more, can be found in the Play Store.