Does nuclear propulsion applied to military ships fall under civil or military nuclear power?

Question

From what I know very few countries are authorized to possess nuclear weapons, although a few others might secretly have some. But using nuclear power for civilian use (to produce electricity) is allowed for mostly any country, as long as they proceed with care.

But what about nuclear-propelled military icebreakers/ships/vessels/aircraft carriers that do not hold nuclear bombs?
Those aren't weapons of mass destruction, but do they fall under military nuclear power?
The nuclear reactions going on in those engines are perfectly controlled, and are mostly the same as those used in civil reactors.

Answer 1

The treaty you're thinking of is the Treaty on the Non-Proliferation of Nuclear Weapons (also known as the NPT or NNPT). The core of this treaty for non-nuclear weapon states is Article II, which says

Each non-nuclear-weapon State Party to the Treaty undertakes not to receive the transfer from any transferor whatsoever of nuclear weapons or other nuclear explosive devices or of control over such weapons or explosive devices directly, or indirectly; not to manufacture or otherwise acquire nuclear weapons or other nuclear explosive devices; and not to seek or receive any assistance in the manufacture of nuclear weapons or other nuclear explosive devices.

As you can see, the limit is on "nuclear weapons or other nuclear explosive devices," not on all military applications of nuclear power. Another provision of the NPT reinforces this. Article III requires non-nuclear weapon states to enter into safeguards agreements with the IAEA to ensure that peaceful applications of nuclear energy aren't diverted to make nuclear weapons. In the guide to these agreements (IAEA INFCIRC/153), paragraph 14 covers use of nuclear material for military purposes. Countries are generally expected to notify the IAEA if they're doing this and give assurances that they won't use the material for weapons, but other than that it's perfectly fine to use the material for non-peaceful purposes. The country does not have to tell the IAEA any classified details about the use or get their approval for the military activity, just that X amount of Y material is being used for military purposes. Countries have used this provision when considering naval propulsion in the past.

Countries might also take the position that naval nuclear propulsion is a peaceful use (which would make them subject to safeguards, but might give advantages under other treaties). For instance, Brazil and Argentina entered into an agreement (INFCIRC/395) to exclusively use nuclear power for peaceful purposes, but in Article 3 declared that nuclear propulsion is a peaceful use. In their IAEA safeguards agreement (INFCIRC/435), Article 13 essentially restates paragraph 14 of INFCIRC/153 but changes some terms to be consistent with that position. "Material not subject to safeguards" becomes "material subject to special procedures" and "non-peaceful applications" becomes "nuclear propulsion," but it's otherwise basically the same. Whether or not nuclear propulsion is a peaceful use, this agreement (which the IAEA signed) shows that it's fully compatible with the NPT.

Because naval propulsion is exempt from detailed monitoring under safeguards agreements (all military use is, but naval propulsion is basically the only practical military use for nuclear energy other than weapons), it's been brought up as a potential loophole in the NPT. Naval propulsion also tends to involve much more highly-enriched uranium than civil power, so the concern is that a country could divert highly-enriched uranium from naval propulsion and use it to build weapons. However, the current rule is that naval propulsion is absolutely an acceptable use for nuclear power even by a non-nuclear weapon state.

Answer 2

Nuclear reactors powering the ships engines are not nuclear weapons.

From Britannica:

nuclear weapon, device designed to release energy in an explosive manner

Nuclear reactors on ships are not designed to produce a nuclear explosion in the face of the enemy. Nuclear bomb and nuclear reactor are different devices. This applies also for military machines using nuclear power just for propulsion.

Answer 3

So Nuclear power in military vessels are considered military nuclear devices because all of the technician making sure the reactors are working properly are military personnel. The use of nuclear power over conventional is because they can provide a lot of power to speed (U.S. Supercarriers are often deployed quickly, and all Aircraft Carriers are capitol ships... in fact, Battleships are no longer a part of modern Navies because Carriers do their job better.). With Icebreakers... speed is desirable as you can clear ice faster... and the Russian/Soviet Navy's greatest historical weakness is a lack of warm water naval ports. Nuclear submarines come in two varieties: Attack Subs, which hunt other subs and Boomers... which... make things go boom... the later actually is designed to launch Nuclear weapons. While the power systems help immensely, they aren't directly influential in a SLBM being launched. The use of nuclear powered engines offers two benefits: It's quieter than conventional deasil to the point that it's almost too quiet... some subs can be detected because there is not enough background noise where they are... AND they can run for a lot longer than deasil without needing to surface for air. To put it into perspective, a convential sub will need to surface at least once in a 24 hour period so the engines can breath... a Nuclear Sub needs to surface once every six months... so it can dock at port and resupply on food and water for the crew compliment.

The later ability of nuclear powered subs is why Nuclear subs carry Nuclear Missiles. In an all out Nuclear War, the best defense against being attacked... is having enough nukes to survive to attack the enemy right back... Mutually Assured Destruction... M.A.D. With Ground missiles, their launch sights are stionary and positions are easy to know... same with aircraft launched bombs... they have to land somewhere... but SLBMs... you can hide those anywhere on 2/3rds of the planet, for six months at a time... and move them to reposition closer to a new possible threat location... And the next time your enemy with nukes rattles sabers at you, you can tell them that you have nukes that could be somewhere close to their coast.

And then... aircraft carriers aren't equipped with Nuclear missiles... but at least in the U.S.'s case there's a lot of threat when they can move a 4,000 personnel naval airbase with enough power to light a city and enough air power to grant air superiority around it and air attack away from it... and it may or may not be carrying nuclear gravity bombs... but certainly will never tell you if they are at that time... eff around and find out if you dare... and they are protected by escorts, if you want to try and sink it... that cover attacks from above, on, and below the sea... and if you do manage to sink one... there are 10 more where that came from. One of which is named after the guy who was famous for Speaking Softly and Carrying a Big Stick... just to make the meaning was clear if one shows up near your shore line...