If there is an issue between SE and EoS, it may be semantic, rather than grammatical. Classically, the first word moderates the second: so, in SE, 'systems' appears to moderate (describe the type or flavour of) engineering; and in EoS, 'engineering' appears to moderate (describe the type and flavour of) systems. Would it were so straightforward, however: both 'systems' and 'engineering' are highly ambiguous terms, meaning apparently whatever their user seems to want.

So, better perhaps to treat both 'systems engineering' and 'engineering of systems' as portmanteau terms, and look instead to their origins, history and heritage to see what each is about. Even then, however, confusion reins. The first of these terms to arise was 'systems engineering,' back in about 1941 in Bell Labs in the US. The term was coined when it was realized that the interconnecting network between a set of nodes could be seen, not as separate parts, but as a whole entity, with characteristics and properties. Or so the mythology tells us.

Subsequently two strands of SE emerged: the first appears to have been 'control systems engineering,' inspired perhaps by the, then, interest in cybernetics. Shortly after, there followed 'systems engineering' without any soubriquet - so a general, or generic, pursuit. This, it seems, may have been inspired by developments in systems science, leading to ideas of systems theory, systems thinking and open systems behaviour. It came to prominence with NASA's Gemini and Apollo missions, both of which were concerned, less with money, more with achieving the difficult-to-seemingly-impossible.

These two strands of systems engineering developed side by side, with not too much in common. Control systems engineering (CSE) was very much about technology. Systems engineering was, by contrast, not necessarily about technology at all, concerning itself with the formation, organization and behaviour of wholes, how to manage complexity, promote harmony between interacting entities, and more. Because of its vaunted ability to 'cope with complexity,' which it had demonstrated amply on Apollo, systems engineering (SE) became the 'tool of choice' for developments in atomic energy, defence and aerospace. So, SE became associated with 'big,' 'complex,' and 'expensive.' Not that SE was necessarily any of those things per se.

However, big, complex and expensive (the latter not being relevant during Apollo) required that the financial folks got involved, and the DoD in particular commenced to surround the systems engineering nucleus (what we have been calling here the 'essence of systems engineering') with all kinds of bureaucracy, concerned with exercising control by a suspicious customer over a non-trusted contractor. (Unpalatable, but true nonetheless.)

So, today, while you will find no mention of stakeholders, or customers 1 and 2, or CMMI, MOEs, or any such in the essence of systems engineering (well, not in my version, anyway) you will find so many bureaucratic overlays and underlays surrounding the essence, that you may find it difficult to even discern the essence of what systems engineering really is. For instance, few practitioners seem even aware that the MOE Cost-effectiveness, is invariably less effective than the ideal. 

Meanwhile, control systems engineering (CSE) had been waxing and waning as interest in cybernetics rose and fell. However, the term 'systems' seemed to 'add lustre to one's cluster,' so there emerged various flavours; electrical systems engineering; electronic systems engineering; computer systems engineering; manufacturing systems engineering; even business process reengineering. The difference between, say, electrical engineering and electrical systems engineering? Honestly? Very little. Somehow there was kudos in using the term 'system' in your title.

To confuse even further, there arose the 'systems house' - very popular in the second half of the 20th century. The systems house often undertook so-called 'turnkey projects,' in which the customer presented a problem, and the systems house undertook to provide the complete solution to the problem - everything, including manpower, training, technology, support, operations support... everything.

The systems house was, by definition, independent, however. It prized its independence so that it could choose products for its final solution from any supplier, without fear or favour. Similarly, if it needed parts to be made, it could put their construction out to competitive tender, to get the best deal for its customer. And, it would necessarily monitor the engineering contractors' work to ensure it stayed within spec. and budget.

Now, if you examine the last paragraph, you will realize that systems engineering - from the systems house perspective - actually included any engineering development and production that might be needed. In that context, engineering of (the technological part of) systems was part and parcel of systems engineering.

To complete its turnkey solution, the systems house would bring together all the many and various parts to form the whole solution. That would include trained people, documentation, training simulators, organization, operational strategies, etc., etc., such that the new system could 'hit the ground running,' i.e., be up and running in short order.So, while some might consider that the Engineering of Systems occurs after Systems Engineering, I will aver that Systems Engineering includes everything, including the design, development and manufacture of products specific to the system, and also includes the integration and setting to work of the resultant whole, people, facilities and the whole shebang.

As to synthesis, that refers, by definition, to the combining of two or more entities to make something new. It is generally contrasted with analysis, which again by definition is the process of separating something into its constituent elements. So, synthesis is combining; analysis is separating. And by extension, synthesis is systems engineering, analysis is engineering. And a system is a synthesis. 

Confused? You soon will be...