The Oracle DBMS is actually more similar, in fact quite similar, to PostgreSQL. I've heard rumors that in fact, they came from a common root.
MySQL is quite a bit different, and for a long time it lagged in advanced features such as transactions.
But thanks to SQL92 standards, the biggest differences are in the functions and the stored procedures. One reason why I discourage the use of stored procedures. Can't help it about the functions, though.
I have an O'Reilly pocket guide to the popular SQL databases that helps me a lot in keeping track of what goes where, as it covers PostgreSQL, MySQL, Oracle and DB2 and I've worked with all 4, sometimes more than one in a day. But I couldn't get interviewed for a job because the HR department wouldn't accept anything but Oracle experience and that was before I ended up at another company doing Oracle on a daily basis. I hate HR recruiters.
If you're interested, the ISBN is 0-596-00512-1 for the March 2004 edition. Hopefully there's a newer one now, but that old one works for most of what I need, with an assist from the Internet.
The Mysql CLI equivalent to SQL*Plus is simpy "mysql". There's also a mysqldump utility that's good for backups and transport. And last I checked, neither Oracle nor DB2 came with such a civilised feature. Couldn't even move DB/2 from iSeries to eSeries. Had to use an ETL tool.