Seems you're learning too many new topics at the same time.
Ok. I'll try to answer.
SQL stands for 'Structured Query Language', and serves as a 'standard' for many vendors that in much ways respects its fundamentals. Oracle, MySQL (now owned by Oracle), MariaDB and PostreSQL are some vendors.
Main thing with SQL code I would recommend you to identify every time you look at it, is to understand if it belongs to DML or DDL. DML stands for 'Data Manipulation Language' and refers to SQL instructions which 'modifies' data. DDL stands for 'Data Declaration Language' which defines or 'alter' de structure on which data will be stored.
Another important concept is atomicity of data manipulation. You can confirm a change or roll it back before it is persisted. This thing corresponds to 'commit' changes or do a 'rollback'. It's some kind of advanced concept, but generally happens "automatically" with standard client configurations. Later, you would have to know about it while programming some system module which interacts with databases.
When you think of the SQL 'server', it refers to the software configured/installed which has the responsability of manage persistence of data within some kind of 'instance' of persistence, allocated in some system with data storage capabilities. AWS implements this service in the cloud, and RDS is the product which supports many kind of SQL flavors to choose (Oracle, Postgresql, etc.)
If you are comfortable with Docker, I recomend you learn the basics which would help you setup and destroy databases many times, which is useful to develop and test locally. Next command, let you start a Postgresql database configured with open port 5432. You can see the server log through docker and use some SQL client to get connected. When you press Ctrl+C everything will be deleted. Of course there are other ways to keep data persistent, but this command would be an easy starting point.
$ docker run --rm -p 5432:5432 --name some-postgres-container-name -e POSTGRES_PASSWORD=mysecretpassword postgres:13.3
Side note: it's better to get used to work with specific docker image versions always (not 'latest').
More details of it usage here: https://hub.docker.com/_/postgres/
if I'm using PostgreSQL, do I also need a SQL server to go along with
it? Is PostgreSQL a language, a server, or both? Is there even a SQL
language or is it only servers lol? I'm genuinely trying to figure
this out myself, but basically everything I read is beyond my scope of
competence and confuses me more. I'm learning the syntax of SQL well
enough, but I'm so confused about everything on the most fundamental
level.
By the way "SQL Server" is Microsoft's SQL flavor, just another one. Don't be confused with the concept of having some SQL server configured.
Yes, you can think of PostgreSQL as a language too, which shares most of its syntax and semantics with other SQL vendors. Yes, there is a 'basic' SQL language shared and compatible between all vendors; some share more aspects than others. In terms of Venn diagrams, you can think of many circles representing each one, Microsoft's SQL Server, Oracle SQL, PostgreSQL, MySQL, etc. sharing the very most of its elements, where each element is a SQL instruction.
When dealing with Databases in general, keep in mind that they helps to modelate situations of 'real world' scenarios or software systems. SQL allows to 'talk' to implementation of "Relational Databases" wich is one kind of database modeling, but there are others too. ER Diagrams helps to represent the 'structure' of a database in a conceptual manner. I like DBeaver because it has an integrated ER diagram generator wich helps to understand the structure of a given database instance.
