Norman castle building in its early phase within Britain (and later Ireland) differed fundamentally from what had become the architectural norm in France in that it tended to be executed by newly ascendant warlords in particular areas who were putting a priority on taking over existing strongholds and strategically advantageous positions in the landscape as quickly as possible. The result was that existing burghs, which tended to be made of stone, were simply beefed up with extra walls and battlements. However a far more typical "castle", especially where none had existed before, was initially a wooden construction using ditches and ramparts that Julius Caesar himself might have been familiar with.
From the reign of William Rufus onwards in England and Wales, and especially under Edward, the first "mega-castles" started to appear. When built from scratch these tended to conform architecturally with Norman castles in France. However they show much more variation than in France in that they were often pimped up versions of existing fortification on particular sites. They also had an advantage over existing large French castles in that the new construction could more immediately incorporate defenses against the latest siege and assault weapons entering warfare.
In Ireland castle architecture under the Normans took a slightly different trajectory. The first wave of Norman warlords did much as they had done in England. However after a few generations many of these warlords' families had begun to become assimilated into Gaelic culture and politics to a degree that alarmed their relatives back in Britain. This led to a "second wave" of Normans (sent often by the English king Edward and some of his successors) who targeted their Norman counterparts and who, when they successfully ousted their predecessors, set about some rapid and quite impressive redevelopment of their own. Some of these redevelopments reflect the fact that they had, through warfare, seen their own traditional defences from an assailant's point of view, and introduced on that basis some rather unique innovations of their own based on this experience. In Ireland therefore one sees from this period a tendency to obliterate and completely replace the existing Norman structures with new ones (one sees this in Wales too for similar reasons), which led to what might be called a "typical Irish" Norman phase of architecture.
The whole thing was probably about to even itself out in terms of architecture throughout all the areas of Norman dominance when gunpowder arrived and changed the rules completely overnight for everybody.
The truth is therefore that one rarely if ever finds a "typical medieval castle" in these places, or anywhere in Europe for that matter. The basic requisites for a successful defence of an enclosed space using the most logical materials and designs available to builders lend an air of uniformity of style to the castles that are lumped together as "medieval", but it is rarely one finds such a castle that hasn't also often incorporated some unique solutions to its own particular location and role in that area, which can range from particular topographical restrictions to its owners' level of participation in establishing a feudal economy and social structure within which the castle would also play a central administrative part.
In fact I would say that this level of investment in "feudalism" as a politico-economic standard is probably that which most dictated uniformity and divergence in terms of architecture in the early medieval period. One only has to take a "typical" French castle and a "typical" Irish one from the 12th and 13th centuries to see the essential differences this caused. Defensively they exhibit similar features of course, but their size, location, adornments and extent of ancillary building show two very different approaches being taken in both locations.