What is the difference between a WordPress theme and a Framework? Which provides the best ease of use for the do-it-yourself non-coder?

The primary distinction is:

1. A theme implies a ready-to-launch WordPress theme with design, back-end functionality, and anything else you might need (according to the theme author's discretion). "Theme" can be roughly equated to "plug-and-play" in the WordPress world.

2. A framework is a set of tools to assist in building custom themes rapidly by handling common challenges ahead of time. "Framework" can be roughly equated with "toolkit".

HOWEVER.

WordPress is an enormously popular, extremely accessible platform, which means that not everyone who builds for WordPress actually A) knows the difference between a theme and a framework, or B) actually did a good job of implementing anything that's promised.

That means that for every high-quality, no-hassle theme or framework you'll find, there are dozens more that are fragile (e.g. can't stand up to even light customization) or just plain terrible (e.g. full of security holes, silenced warnings, bad practices, etc.).

Popular frameworks like Genesis have large contributor networks, which cut down on poor quality and security risks. But for a non-coder, the learning curve may be a little steep.

The best solution may be to evaluate the cost of getting your current theme audited for quality by a professional coder with a good reputation in the WordPress community. I'm not familiar with the theme you're using, but it's possible that it's a great theme that's well-built. If that's the case, you can keep using it even if the theme creators were to suddenly disappear (though not for long, as there's always a need to modernize themes as WordPress matures and PHP marches forward).

If the theme is NOT well-built, consider having a pro build something quality that's specifically suited to your needs. This costs money, but you have to weigh that against your revenue (and the potential loss of it if your DIY site collapses in on itself unexpectedly).

Otherwise, do your homework and read reviews from the users of the various themes and frameworks you're considering. Contact the positive reviewers directly to determine how closely your level of skill and comfort with WordPress resembles theirs. That's important, because what I can do comfortably with WordPress (after a decade of building custom themes from scratch) will be very different from someone who's only comfortable using the theme customizer.

Sorry if this is a little overwhelming; this is a big topic with a lot of pitfalls and challenges down every path. It ultimately comes down to whether you'd rather spend time or money to solve problems, and which will ultimately end up costing you more.

If you'd like to go into the specifics of any of this, or if you want to discuss your theme in particular, hit me up for a call.

Good luck!

I focus on SEO. That said, I can create websites in HTML5 and CSS3. In the last year I have also spent a lot of time modifying WordPress themes.
I never liked Elegant themes. They are beautiful themes but funky. It's like Elegant doesn't give 100% theme design for free. There's always something you need to buy. That said, Divi is beautiful, but it too is a little funky. The demo has a lot of animation which makes it jumpy and a little slow.
Page speed is an SEO factor.
The Genesis framework is built for SEO. Those guys are SEO geniuses. But if you use the Yoast SEO plugin (free version is enough) you will have serious SEO help on any WordPress theme.
LayersWP looks interesting. I don't need drag and drop but I might check it out myself. Their demo page is not jumpy nor slow. Doesn't look like its a framework like Genesis, more like a theme you can modify. That is, it doesn't have a built in SEO piece like the Genesis framework. But again, get Yoast.
Finally, with the Genesis framework you will still need a theme, and now you'll need a Genesis theme. Not real thrilled with Genesis themes. Design is not their forte. They are SEO.
Hope that helps. It was a good question. You are on the right track.
Not sure what "theme-locked" means, exactly. I just skipped that part of your question. Forgive me.
If you'd like to talk more just call.

The line between a simple theme and a framework is as much about product development philosophy and definitions as it is about user workflow. Themes are closer to the typical end user in intent, and are designed to be self-contained, focusing on GUI based customizations. WordPress Frameworks tend to target professional designers and / or developers rather than casual users. They are usually built around a core theme that whose design is often plain. Like most themes, they have GUI settings and options. But, they also allow extensive modifications using hooks and filters that developer find useful.

Frameworks themes are often accompanied by a growing collection of leaner child themes. These provide design variations, and sometimes special functionality for particular markets, such as restaurants. This describes the Genesis approach which also includes a large number of plugins that add extra functionality. If any of its many available child themes fits your needs with little modification other than styling, Genesis is a great choice. There is also a great community and support for anything needing more advanced customization.

LayersWP is a bit of a different animal. It is a framework capable of supporting child themes but also adds a powerful integrated page builder to the equation. Page builders are a relatively newer trend in the WordPress ecosystem. They focus on layout and content of individual pages or posts. Often they include front-end editing capability and drag and drop modules of content. So there are very friendly to DIY non-coders and editors.

Sometimes this comes at a cost. You can be "locked-in" even more by a page builder than with a theme if they use tons of short codes to build your individual pages. And they can add bloat to your source code. Most are available as separate plugins, but LayersWP approach seems to create a much tighter fit and works with widgets to build pages. Their goal seems to be to build a thriving commercial ecosystem of add-ons, styles kits and themes around the free LayersWP core. So, if your site needs a page builder and you can live with being lock-in to its growing ecosystem, layersWP could be your answer.