They are different ways of doing practically the same thing. In your .htaccess you would set up the /index.html to be 301 redirected to yourappliancerepairla.com. Which will redirect any user that lands on /index.html to yourappliancerepairla.com.
The canonical tag doesn't redirect the user to the homepage, but it tells google or any other search engine that the "original" content is yourappliancerepairla.com rather than /index.html or /home.html or www.yourappliancerepairla.com and so on.
I would give the edge to canonical tags, but 301 redirects in the .htaccess file do have their use.
Looking at your site (viewing the page source) your home nav link is pointing to /index.html you can change that to http://yourappliancerepairla.com or simply " / " that change might actually fix your issue... but I would still put a canonical tag in the header of index.html for defensive purposes. Also consider placing a canonical for all your pages as a defensive mechanism to duplicate content.
It's considered a duplicate because index.html does exist, index.html is the physical file of the homepage where you change code. All of these pages are possibilities your homepage (there are more):
http://yourappliancerepairla.com
http://www.yourappliancerepairla.com
https://yourappliancerepairla.com
https://yourappliancerepairla.com
http://yourappliancerepairla.com/index.html
http://www.yourappliancerepairla.com/index.html
There are more possibilities. That is why the canonical tag is important here. Also consider google search console and setting up properties for http non www, http www, https non www, and https www all pointing to the preferred version of your site which would be the http non www.
