Is there a Federal Army? It may be that the FedMar is the more Federal of the two surface components. I can see the Federal Army being a catch all for planetary defense forces, who as part of the Federation utilize a common set of standards and doctrines. They however are there to protect their home planets and rarely are called upon to leave.
The FedMar is mobile, highly trained, spacefaring, drop podding, component specialized in executing rapid strike missions to cripple the command and control nods of organizations that threaten Federal security (to include the occasional rogue Federal Army Planetary Commander perhaps!). They have a tight and well oiled relationship with the Federal Navy.
This article mentions the existence of the Federal Army. I think your interpretation is spot-on actually. It might be similar to
Eurocorps and
EUFOR, just without the 'rapid reaction' bit. Although it is not Federal in the sense it directly answers to the President (as you said), it may be federal or confederal in terms of structure, rather than a singular entity like the other two branches.
As for that description of FedMar, heh, I would like to claim a monopoly on that, but I'm sure all of the marine forces are like that...or maybe not. The Amarr might just "bombard from space", whereas the Caldari as a defensive force might want defeat the enemy in space to prevent warfare ever needing to occur on the ground in the first place (fits in with that mention about how Caldari ground forces are poorly-equipped, and the lightning warfare bit). Ofc there'll be variations between the 8 megacorp security forces, but I think they'll be a grade lower in capabilities compared to a nationally-funded force (like the Fed marines). Or rather, Home Guard might be excellent at station boarding for example, better than FedMar, but FedMar have a much broader pallet of capabilities.
I think one of the challenges for the State side of things is there are 8 PMCs which likely have a wide variety of subordinate PMCs with various specialties. The State Peacekeepers are likely just the ground component of the State Protectorate. The Caldari military organization is interesting because it very much depends on how one views the State as a whole functioning. The CN for example is funded by the CEP and so presumably the CN's "board of directors" is CEP appointed.
Being the ground component of the State Protectorate sort of keeps it consistent with the name (considering they seemingly prefer using 'Caldari' as the traditional national prefix in general, not State). And yeah I think the lack of CCP guidance on these specific matters means it is down to a bit of interpretation. If we assume the State Protectorate is Heth's baby, for conquering and destroying the Federation (something the Caldari Navy is not really purposed for; ignoring the jingoism from the admiral in Dark End of Space chron), then the State Peacekeepers are an extension of that. Deliberately using propagandistic names that go against what it's actually intended for also fits in with the Heth doctrine. The State 'Protectorate' isn't protecting since it says it's going to go out there and conquer...similarly, the State Peacekeepers will be conquering Gallente planetside territories rather than said UN-style humanitarian stuff.
So it's a case of another layer of factionalism within the State, this time in the military and not corporate. Caldari Navy/Army might be more traditional "Defend the State!", whereas State Protectorate/Peacekeepers are Heth's radical "Destroy the Federation!".
Also with regards to civilian control...another ambigious area. Might fall under CEP, but given the fact the State was founded on militarism and war, the Caldari Navy might occupy an independent status not dissimilar to those found in dictatorships IRL. They might consider themselves Caldari traditionalists that do not concern themselves with corporate warfare/"petty disagreements", and are concerned with the Caldari people as a whole. It might be that they receive orders from the CEP, but "war room control" is done by Caldari admirals, not senior politicians as in the Federation. I imagine CEOs might try to intervene in military C&C, but they are rebuked as "The safety of the Caldari people come first, not your quarterly profits". This emphasizes the efficiency amongst the Caldari, versus when civilian leaders in the Fed go "You can't just bomb the enemy, those are my constituents down there!" making them less efficient but more '''''humane''''.