Auguste Kerckhoffs said it all in his La Cryptographie militaire (1881). David Kahn, speaking of Kerckhoffs in The Codebreakers, says that he:
...made the requirements that have come to be demanded of systems of
military cryptography, requirements such as simplicity, reliability,
rapidity, and so on. This clear recognition of the new order
constitutes Kerckhoffs' first great contribution to cryptology.
Kerckhoffs revolutionized military telegraphy and set it apart from the rest.
Much more recently, Bruce Schneier made an interesting distinction between academic and military cryptography--and their courses of development:
"Academic cryptography is mostly based on Feistel's work in the mid-1970s at IBM: SP-networks and Feistel networks. Military cryptography started with rotor machines, and then generalized into shift registers... I find it fascinating that the two different design paths are converging." 
What Mr. Schneier meant was that modern military cryptography developed out of rotor devices such as the Hagelin machines (for example, the M-209) which were replacements for earlier systems such as the M-94 cylinder. This cylinder and the M-138 strip ciphers saw extensive use during the 1930's and all of World War II, but they are seldom discussed today. Incredibly important traffic-- that of the Manhattan Project-- was encrypted with the M-94. What is it the distinguishing feature of these systems? They are portable and lightweight.
Being lightweight was, and still is, extremely important for military cryptographic systems. The German Schlüsselgerät 41 (SG41) was superior to Engima, but it weighed about 30 pounds, and was therefore too heavy to deploy for frontline use.
Modern military encryption often focuses on radio and satellite communications, but it depends on what country one is talking about. For some it might just be radio. Encrypted military radio systems tend to send traffic via some method of spread-spectrum transmission such as frequency hopping. This is sometimes done to prevent jamming (denial).
Authentication is extremely important; metacontent is too. Plaintexts are usually highly structured, and acronyms are very common. The best encryption a country has in stock will probably be used for command and control by senior leaders. A lot is at stake.
The adversarial nature of cryptography, its essence, is clearly seen in military information security.
Compromise can have immediate catastrophic results. Military encryption is often done as half of a skill set, the other half being cryptanalysis. The viewpoint of the attacker can be developed, which is precious. In very general terms, military encryption today is surprisingly aware of the history of cryptography because of what one might encounter or need to use downrange--most of today's conflicts are asymmetrical. Classical cryptography is still being used by certain groups.
Military encryption usually takes place in a wider security context that is very substantial and includes strong physical security, careful key management, and counter-intelligence.
If we include the encryption methods of insurgents, paramilitaries, and other such actors under military encryption, then we see a reliance on classical methods such as code books. Serious people such as NVA Special Forces were known to use one-time pads and HF radio. In military matters what is often needed for immediate success is just something simple and dependable--and that applies to encryption too. Forward secrecy may not always be the biggest concern, especially at the squad/platoon/company levels, and it has to be fast and simple (not a VIC cipher, for example).