OpenJDK for production and LTS?
LTS is supported for 3 years and will receive updates until it expires. When you use openjdk you need not pay for support or patches. I always go with LTS like java 11.
The non-LTS version will have newer features but they are short lived like 6 months. They don’t receive updates for long rather it is expected to upgrade to next version. Security patches are available on same version or next version.
If you don’t have a special usecase then open jdk is more than enough
OpenJDK is a free and open-source implementation of the Java Platform. The implementation is licensed under the GNU General Public License. You are free to use at any environment. But you won't get any kind of support from the Oracle and you've to rely on open communities support, later can be best than the OEM support some times.
LTS is a product life cycle management policy in which a stable release of software is maintained for a longer period of time than the standard edition. You get security updates for some good number of years.
Do you have to pay to use Java?
Answer is yes, Iff you use Oracle JDK for business, commercial, or production purposes.
Answer is No, if you use OpenJDK irrespective purpose or environment.
PS: this is all about licensing and it can change over a period of time.
I wrote a blog article discussing that topic in early 2019.
First, as far as I know, the OpenJDK team does not offer any premium support.
Second, normally one goes to the LTS for longterm support, mainly security updates.
Third, Oracle will only hand over the code for the LTS version to the OpenJDK team and only after the LTS has reached its end of life. This means that the OpenJDK community has to keep up with changes on their own.
Now to the topic on the JDKs being identical. They both pass the JCK and thus can be used as drop-in replacement for each other. The implementations, however, may vary.
There is a host of JDK providers, all with different support plans. Fact of the matter is, there is no free lunch. If one wants support, one has to pay.
A remark on your post: Please limit yourself to one question per post