Are "functional units" the same as "issue slots"?
Both of these terms are generic - they don't, in isolation, have any well defined meaning. A 'functional unit' could be anything from a edge-detect/trigger module up to a whole CPU.

Functional units are just a grouping of logic with an easily defined purpose. The level of abstraction is up to the person using the term.

An 'issue slot' does imply some degree of parallelism in the design, although it is ambiguous what is being issued. Most likely a micro-op, or (less likely) a bus transfer but this shouldn't be assumed. How the issue slots are 'driven' is also not defined. They could be split by function, driven from a buffer/queue, etc.

The question implies a more fundamental gap in the description which you're trying to interpret. It's possible that the structure presented to you is more important than the way it was described.