What they did was change the update model for paid versions of the standard Oracle JDK -- you must have a commercial license with Oracle in order to receive security and bugfix updates for copies of the Oracle JDK.
OpenJDK, on the other hand, was unaffected by this change; things like security mitigations/fixes land in OpenJDK, and make their way to other versions (like older JDK versions, or Oracle enterprise copies) from there. So, you can go download Zulu or OpenJDK binaries from your distributor (such as your Linux distribution) and you'll be fine (assuming they update promptly).
There are also feature distinctions between the Oracle JDK and OpenJDK, but they have been getting smaller over time -- AppCDS and Flight Recorder, which were Oracle-customer-only features, for example, are now in OpenJDK proper (FR will come in JDK 11), and many features such as ZGC (and originally G1, too, I think) were developed in the open and went into OpenJDK directly, right from the start.
If you're just running a bog standard Linux/BSD system with some Java software on it, you're almost certainly OpenJDK already anyway, and your distribution maintainers handle security updates for you.
OpenJDK, on the other hand, was unaffected by this change; things like security mitigations/fixes land in OpenJDK, and make their way to other versions (like older JDK versions, or Oracle enterprise copies) from there. So, you can go download Zulu or OpenJDK binaries from your distributor (such as your Linux distribution) and you'll be fine (assuming they update promptly).
There are also feature distinctions between the Oracle JDK and OpenJDK, but they have been getting smaller over time -- AppCDS and Flight Recorder, which were Oracle-customer-only features, for example, are now in OpenJDK proper (FR will come in JDK 11), and many features such as ZGC (and originally G1, too, I think) were developed in the open and went into OpenJDK directly, right from the start.
If you're just running a bog standard Linux/BSD system with some Java software on it, you're almost certainly OpenJDK already anyway, and your distribution maintainers handle security updates for you.