Getting specifics in why they differ requires someone to be an expert in bother to be able to compare both. I don't claim to know much of greenplum.
The basic principles which I would expect all developers to learn over time dont really change. But there are "quirks" of individual engines which make specific differences. From your question I would personally anticipate 1 and 4 to remain the same.
Indexing is something which does vary. For example the ability to use two indexes was not (is not?) Ubiquitous. I wouldn't like to guess which DBMS can / can't count columns from the second field in a composite index. And the way indexes are maintained is very different from one DBMS to the next.
From my own experience I've also seen differences caused by:
Different capabilities in the data access path. As an example, one optimisation is for a DBMS to create a bit map of rows (matching and not matching) the combine multiple bitmaps to select rows. A DBMS with this feature can use multiple indexes in a single query. One without it can't.
Availability of hints / lack of hints. Not all DBMS support them. I know they are very common in Oracle.
Different locking strategies. This is a big one and can really affect update and insert queries.
In some cases DBMS have very specific capabilities for certain types of data such as geographic data or searchable free text (natural language). In these cases the way of working with the data is entirely different from one DBMS to the next.