I am trying to understand the difference between setting up Routines as opposed to setting up smartapps? For instance, I have smartlighting app setup to turn on and off my various lights at certain times. But I was watching a video where the guy setup Routines to do the same thing. What is the difference?
No big difference. Routines can be turned into widgets on a smart watch. 
And they appear in their own section in the mobile app. So they’re intended for code which you will sometimes trigger manually by tapping the tile in your phone mobile app or the widget. Although they can also be set up to run automatically.
A smartapp is more often something that you set up and then just runs automatically ever after.
But really routines just get special treatment in the UI, otherwise they’re the same.
With regard to smart lighting, and only smart lighting, it is eligible to run locally if your Internet is down. Neither routines nor other smartapps can run locally at this time. But that’s not a routines versus smart apps issue, that’s just a special feature of smart lighting.
https://support.smartthings.com/hc/en-us/articles/205380034-Routines
https://support.smartthings.com/hc/en-us/articles/206145893-Is-there-a-SmartThings-widget-
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I did learn that I can create a routine and put it as a widget on my phone. I have done this for the hues lights until I can get a motion sensor. Little faster than having to open the app, etc…
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The $25 hue dimmer light is also a nice device. Battery operated so you can put it anywhere. SmartThings doesn’t recognize it, but it connects to your Hue bridge and works as a parallel means of control. Great for guests.
https://www.amazon.ca/PHILIPS-Hue-Wireless-Dimmer-Switch/dp/B0167Z0P3I