Yes, the purpose of the math behind a certificate is to 1. allow for encrypted communications, and 2. establish trust of identity.
- As Rich points out, any of them will do a fine job on encryption, unless you go out of your way to screw it up somehow.
- Your ISP one will establish that you are indeed a customer of the ISP.
- One from LetsEncrypt or similar services will establish that you are indeed the owner of the website.
- A more expensive one will verify that you are in fact the real-life entity you claim to be. There are different levels here too: some will just verify that you own a credit card in that name, others will effectively do a corporate background check.
For a law firm or financial business of any kind, I'd expect the latter. You can see how they appear differently on your browser right now. You should see some kind of lock icon for pilotsofamerica, because it's using a LetsEncrypt certificate. But if you go to
www.bankofamerica.com or similar, your browser should show you some slightly more fancy verification icon that shows that it indeed belongs not just to "the webmaster of
www.bankofamerica.com" but rather "Bank of America Corporation [US]".