@orangebucket has given you a very good answer, I’ll just add a bit of history And a few resource links. 
Back in 2014, smartthings hosted a groovy cloud and customers were allowed to write their own custom code and run it there. That’s also where most of the officially provided smartapps ran.
Over time, some of the officially provided smartapps were moved to local operations on the customer’s hub, Particularly “smartlighting.” To this day, Customer-created code still ran in the cloud.
As smartthings scaled up, Samsung wanted to get rid of the groovy cloud, and it is scheduled to go away by the end of 2021. In Its place, Samsung offered two things: a quite robust scripting language called “the rules API,“ which is still in development, and a new integration API which allows customers to write code in any language they want, host it themselves, and integrate with smartthings through that cloud-based API. There is also still a simpler rules engine built into the smartthings app, which is what you find when you just hit the + in the app and add an “automation.” The built-in rules engine is a lot more sophisticated than the one in the 2014 version of the smartthings app, but the rules API can still do much more.
So right at this moment, the summer of 2021, we are teetering on the edge of a major major transition, which is when the groovy cloud will go away. We don’t have an exact date for this, but it’s pretty clear that a lot of things are going to stop working on that day, and not all community developers are creating replacements.
Most recommendations are that if you are just getting started now, you should start with the rules API or with your own hosted code using the integration API since the Samsung-hosted groovy cloud will be going away soon.
The Terminology keeps changing, but it does sound like they are going to keep the “smartapp“ name for customer written code in the future, but it’s going to mean something very different. Instead of being groovy code hosted by Samsung in the smartthings cloud And added to your account through the IDE, it’s going to be code that you host yourself and integrate with smartthings through the integration API. Many people are using MQTT for this now, and that will continue to work, but you do have other options as well.
Whether it’s the old architecture or the new architecture, you do not have the option to run your own custom code on the smartthings hub.
So… if you are reading threads about coding from anywhere except the new developers section of the forum or the new developers website, it’s going to be referring to the old groovy cloud and that’s not going to do you much good in a few months. So that’s where a lot of the confusion probably arises.
If you’re just starting out now And you want to do more than what the built-in rules engine in the app provides, probably the best thing is to start with the rules API, see if it will do what you want it to do, and if so, move forward with that. Because that code will continue to be hosted by smartthings, and some of it may even run locally on the smartthings hub.
If you need features not supported by the rules API, then it’s probably best to go with the future direction and write your own code, host it yourself, and integrate through the integration API.
There are a lot of links that might be relevant on all this. I’m just going to put a few here and then if you have specific questions we can pull up some of the others that might help. Also note that both the rules API and the integration API are still in development and documentation is not complete. 
LINKS
- Official announcement of the coming changes, including the termination of the groovy cloud
- Developer section of this forum. This is where you’ll see a lot of questions and some answers on what the changes mean for custom development. There are some staff members who regularly post in the section.
- The rules API subsection. There seems to be an attempt to call the individual rules that people create through the wizard “recipes,” But that hasn’t really caught on with the general community yet.
- The new developer website. You’ll need to set up a developer account here in order to use the integration API. Documentation is not yet complete. This particular site uses the term “automation“ for what other smartthings materials still call “custom smartapps.“ (Inconsistency in terminology is a long-standing smartthings tradition.
) Also although that site makes it it look like signup is only available to device manufacturer companies, individual customers can also register for a developer account.
That’s probably enough to start with for now.