You may be interested in these two hour-long videos I have on the matter, covering armor developments in France and the UK.

France: https://www.youtube.com/watch?v=ZqoPZK6gyao

Bottom line: On the tactical level, the French believed that the decisive component in a fight was firepower. To this end, there was great emphasis on co-ordinated movement of all available arms, but particularly, artillery. This was known as The Methodical Battle (La Bataille Conduite). The problem with this is that it required excellent communications for the commanders to co-ordinate subordinate units. It could, in theory, work, but the problems were that French commanders had lousy communications, relying mainly on messengers and telephone instead of radio (Or just driving themselves from HQ to HQ), and a lot of commanders refused to act without orders from above.

On the strategic level, France believed that the next war would be a total war, the winning side being the one which would best be able to mobilise the national resources of manpower and industry. As a result, they built the Maginot Line to defend the industry, which was near the German border, and created a massive army based around conscripts. They were right about the nature of the next war, they just were knocked out before they could get to that stage.

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UK: https://www.youtube.com/watch?v=d7AgcBIs8bM

The British were firm believers in the advantages of mechanisation, and were the only military to kick off the fighting reliant purely on gasoline and not horses. They were the world leaders in doctrinal thought for much of the inter-war period. However, they fell apart on the execution stage in large part due to funding. The ten-year-rule which kept getting extended (Which premised that the UK would not be involved in a major war in the next ten years) meant that there was no money available for the construction of new equipment for experimentation. One year, the tanks might be used as an independent body for the experiment, the next year, they might be used for combined arms experiments, but there was not enough to do both at the same time. As a result, their implementation was sill a little bit rough. They had the right idea, though. Unlike the French, the British were firm believers in the power of the radio.

On the strategic level, the big question was "what's the army for, anyway?'. Colonial policing requirements are different from those of a continental war, and Britain's home defense would be reasonably well done by the RAF and RN. Thus is was only at a later stage that the British really started looking to 'high intensity' warfare as would be found on the Continent, and for that, the primary design requirement was for the British Army to fight alongside France in the event of a German declaration of war. The armored divisions for exploitation were still a bit rough in the design concept, but since the initial requirement was to rush into Belgium and defend, that wasn't so much of a short-term problem.

I have not yet done videos for Japan, Italy or US. It will, however, be perhaps suprising how close a lot of these doctrines (with the possible exception of the french) are to each other, at least after 1941.

The Imperial Japanese army doctrine didn't have a flashy name, but it was designed to fit their circumstances. During the 1930's Japan became aware of advances in firepower and mobility which European armies were incorporating. However, the Japanese army was confronted with three problems in following suit. Firstly, the Japanese army was destined to be under-resourced due to the small and only partially industrialized Japanese economy, which was roughly on par with the Italian economy in the 1930s. Secondly, the Japanese Navy had first priority on industrial output due to Japan's island geography. Lastly, the Imperial Army's intended theater of operations was Northeast Asia (North China, Manchuria, Maritime Siberia) a region which in the 1930s had poor roads and a general lack of transportation infrastructure.

In 1936 the IJA begin a modernization plan under Ishiwara Kanji head of the operations section of the general staff, designed to moderinize the army under these constraints. Infantry divisions became "triangular", meaning smaller, more mobile divisions with a similar amount of artillery firepower as the earlier square divisions. The artillery was modernized with an emphasis on smaller more mobile pieces that could be transported on Pack Animals reducing the need for motorized transport. Larger caliber guns were available but tasked for situations when mobility was not at a premium. Doctrine was focused on high infantry mobility and flanking actions in situations where poor transportation infrastructure was the norm. While the IJA's rhetorical emphasis on morale and spirit has been justly criticized as out of touch with the modern experience of war, it fit well into their doctrine of hard-marching, hard hitting infantry-artillery combined arms.

A known flaw in the doctrinal scheme was that it was designed for short, limited wars. The artillery had limited reserves of shells. Infantry divisions were geared towards readiness rather than deep reserves of trained troops. Knowing their economic situation, the doctrine was designed to win the type of wars they had a chance in, rather than prepare for long wars that senior officers knew might be unwinnable for a smaller country. They planned to win all the initial battles in a short war with either the Soviets or the Chinese and then work out a peace.

Of course, it was the Imperial army's awful politics that dragged Japan into multiple long wars. Yet, Despite the terrible politics inside the Imperial Army and between it and the Navy and the civilian government, the IJA actually created a doctrine that was coherent and adapted to their circumstances. Japan's initial successes in China and Malaysia were in part due to their doctrine, but their long term failure was also predicted by weaknesses in their doctrine to which many Army officers were well aware.

Source: Drea, Edward, Japan's Imperial Army, It's Rise and Fall 1853-1945"