not sure on a moto, but i can do it on my note 8. go to gmail and at the top hit the hamburger(it is the three lines), scroll down to settings, select your email address and not general, select manage notifications. now this will take you to what looks like the notifications settings found in your phone setting, but it is not. it should show you your gmail address and then select sound, and change it to the sound you like.
not sure on texts, but at least you can change the your gmail sound.
edit:
i also was able to change my text sounds as well by going into the app's settings and change the sound. i then checked the general notification sound that i originally set in the phone's settings and it did not change to the sound now assigned to my text messages.
......so now i should have separate sounds for gmail, text, phone calls, and general notifications.