Star Trek:The Next Generation and Deep Space Nine

A first commment I would suggest that the 'Star Treks' portrayed
show roughly three or four different 'timelines', basically
depending on whether you include "Enterprise" (a.k.a "Shitterprise")
or not.

The 'first', introduced by Next Gen fully and expanding on events
in TOS, describes the 'Trills' as being a relatively unknown race,
presumably new to the Federation, and the peace/alliance between
the UFP and the Klingon Empire as being also a relatively recent
development, following various conflicts between the Klingons
and Romulans of which the Federation was not a part of (and
who presumably would directly or indirectly aid an ally).

The second is more developed and could probably be considered
canon as it concerns characters in 'TOS' and 'DS9' who are
present in "The Undiscovered Country", referring to 'Curzon
Dax' (a Trill Federation ambassador) and his participation
in the signing of a peace treaty between the Klingons and
the Federation 70-odd years previously.

What can be made (rough) sense of is the relationship
between 'commisioned' and 'non-commissioned' ranks
in Starfleet, basically assuming that the rank of
'Ensign' for all three divisions are equivalent
but this changes until the apparent 'proper'
commissioned ranks of 'Lieutenant' (Commmand),
'Lieutenant-Commander' (Engineering and Security)
and 'Commander' (Medical and Science )

Thus, three 'non-commissioned' chains of command
can be surmised for the three divisions (cadet refers
to all Starfleet cadets);

Command
1.Lieutenant (junior grade)
2.Ensign
3.Yr 4 cadet
4.Yr 3 cadet
5.Yr 2 cadet
6.Yr 1 cadet

Engineering and Security
1.Lieutenant
2.Chief Petty Officer
3.Lieutenant (junior grade)
4.Petty Officer
5.Ensign
6.Engineering or Security Rating


Science and Medical
1.Lieutenant-Commander
2.Lieutenant
3.Lieutenant (junior grade)
4.Ensign
5.Enlisted First Class
6.Enlisted Second Class
; with 'Command' apparently outranking 'E/S' and 'M/Sci'
in the overall chain-of-command, so a rough comparison
with Terran commissioned and non-commissioned ranks
can be given:

1.Captain=Colonel

2.Commander [C]=Lieutenant-Colonel

3.Commander [E/S]=Major

4.Lieutenant-Commander [C]=Captain

5.Lieutenant-Commander [E/S]=1st Lieutenant

6.Lieutenant [C]=2nd Lieutenant

7.Lieutenant (junior grade) [C]=Regimental Sergeant-Major

8.Lieutenant [E/S]=Sergeant-Major

9.Lieutenant-Commander [Sci/M]=Senior Warrant Officer

10.Chief Petty Officer=Warrant Officer (Class One)

11.Lieutenant (junior grade) [E/S] /Lieutenant [Sci/M]
=Warrant Officer (C2)

12.Petty Officer=Staff Sergeant

13.Lieutenant (junior grade) [Sci/M]=Sergeant

14.Ensign=Acting Sergeant

15.Yr 4 cadet/Engineering or Security Rating=Corporal

16.Yr 3 cadet/Enlisted First Class=Acting Corporal

17.Yr 2 cadet/Enlisted Second Class=Lance Corporal

18.Yr 1 cadet=Private