Local Channels coming from the Roku TV compared to 'local channels' I see on my cable provider.

You are paying for local channel access through your cable company. 

The channel apps local stations make available for streaming services like Roku often only contain rebroadcasts of their local news and weather.  They likely do not have the rights to stream network (ABC, NBC, CBS, FOX) programming

If you are where you can pick up your local channels via an over-the-air antenna connected to the antenna input on your Roku TV (or non-Roku TV for that matter), you can get live broadcasts of your local channels that way for free.

If not, you'll have to continue to pay for a subscription to a service that carries your locals.  Many cable systems have a lower cost "lifeline" tier that includes just locals and a handful of other channels like weather and CSPAN.

Otherwise, you'll have to pay for a streaming service that carries your locals.  Check what's available from Youtube TV, Sling, Hulu Plus Live TV, Fubu TV, etc to see which ones have the local channels you want.