I might not be able to distinguish the difference between processors and sysplex images.
I think one issue is terminology. A processor is a machine and may have anywhere from 1 to 141 LPARS on it. A sysplex is a set of LPARS that communicate via cross-system coupling facility (XCF). It is easy to distinguish between processors and sysplex images -- a processor is a physical box while a sysplex image is software running on one (or more) boxes.
WLM has little, if anything, to do with where jobs execute. WLM is used to manage workloads -- as in relative performance of address spaces against each other and against the defined goals -- not to execute jobs. From the z/OS Basics manual at
https://www.ibm.com/support/knowledgece ... hjeses.htm :
The job entry subsystem (JES) helps z/OS® receive jobs, schedule them for processing, and determine how job output is processed.
Batch processing is the most fundamental function of z/OS. Many batch jobs are run in parallel and JCL is used to control the operation of each job. Correct use of JCL parameters (especially the DISP parameter in DD statements) allows parallel, asynchronous execution of jobs that may need access to the same data sets.
An initiator is a system program that processes JCL, sets up the necessary environment in an address space, and runs a batch job in the same address space. Multiple initiators (each in an address space) permit the parallel execution of batch jobs.
One goal of an operating system is to process work while making the best use of system resources. To achieve this goal, resource management is needed during key phases to do the following:
Before job processing, reserve input and output resources for jobs.
During job processing, manage spooled SYSIN and SYSOUT data.
After job processing, free all resources used by the completed jobs, making the resources available to other jobs.
z/OS shares with the job entry subsystem (JES) the management of jobs and resources. JES receives jobs into the system, schedules them for processing by z/OS, and controls their output processing. JES is the manager of the jobs waiting in a queue. It manages the priority of the jobs and their associated input data and output results. The initiator uses the statements in the JCL records to specify the resources required of each individual job after it is released (dispatched) by JES.
IBM® provides two kinds of job entry subsystems: JES2 and JES3. In many cases, JES2 and JES3 perform similar functions.
During the life of a job, both JES and the z/OS base control program control different phases of the overall processing. Jobs are managed in queues: Jobs that are waiting to run (conversion queue), currently running (execution queue), waiting for their output to be produced (output queue), having their output produced (hard-copy queue), and waiting to be purged from the system (purge queue).
JES and z/OS do job scheduling; WLM does not.
because WLM can control the initiators count in any particular image
This depends upon the site -- the systems programmers may have JES controlling the initiators (which means the operators and system programmers in practical terms) or WLM controlling the initiators. Note that when WLM is controlling the initiators, it is managing the initiator count to improve system throughput; it is not doing anything to actually handle the jobs.
then you are saying at the first place the jobs are randomly run in any of the two images as long as those two images also have free initiators.
If you are saying "image" to mean "LPAR" then yes. If you are saying "image" to mean "jesplex" or "sysplex" then largely no. And note that jobs are transient -- so initiators are ALWAYS becoming available as jobs complete. One of the tuning tasks system programmers perform is to set the number of address spaces for each LPAR; this is what sets the limit on initiators and system programmers do NOT want to run out of "free initiators" as you call them. Systems do not respond well to a lack of initiators since they are used for started tasks, TSO users, batch jobs, and OMVS processes.
To some degree, you will remain forever confused. The only ones who know exactly how JES and z/OS handle jobs are those working for IBM in the development groups for JES and z/OS. Unless you go to work for IBM and get into one of these groups, all you can do is read the IBM manuals and hope they provide enough illumination upon the topic(s) you're confused about.