As time and discussion continues here on this forum, I am increasingly led to believe that some here are confused about certain basics of 40K lore regarding the Emperor's Inquisition in the Imperium of Man. So, I humbly submit this in an attempt, to provide some clarification.
Notwithstanding the geographical administration of the Inquisition, the organisation consists of many Orders or rather Ordos (yet another bit of dodgy latin). Of these orders, there are 3 major and, many minor orders. Each order specialises in a peculiar aspect of the Inquisition, though is not confined to it.
The 3 major orders are, the Ordo Malleus who specialise in the threat of daemons from the warp, the Ordo Xenos who specialise in the alien threat of corruption and, Ordo Hereticus who specialise in the internal threat of witches, heretics, mutants and rogue . The minor orders or Ordos Minoris are almost countless and include the Ordo Militum (watches the military), Ordo Chronos (you guessed it, time travel) and, Ordo Hydra which in the end had many of its senior personnel exterminated by the Inquisition after a failed attempt to turn all of humanity into a single hive mind.
The example of Ordo Hydra, why do I think someone had been reading Marvel comics, gives an example of the varying approaches that inquisitors take, primarily between those in the same order. This has become known as The Puritans and Radicals, whilst it is not a simply 2 opposing viewpoints, the differing approaching to combating the threat of chaos could be summed as the radicals believing that you should fight fire with fire' and will thus use chaos against itself. The puritan viewpoint is that the use of any chaos will lead to corruption regardless of intent the beginning of a slippery slope. These beliefs are not simple black and white, but rather varying shades of grey as it were and, many of these philosophies are well known such as Thoronism, Horusism and, the Anomolian Beholders.
Whilst conflict between the Ordos is rare and, I do mean rare, conflict between Inquisitors within an Ordo is not. This is where the Puritan vs the Radical comes into play. For example, one Inquisitor may feel that using a daemon weapon against a daemon is justified, another within the order may 'judge' that inquisitor to be a heretic, corrupted by the chaos, who should be exterminated. However, there are many inquisitors who have less extreme differences of opinion that do work together, forming 'Cells' to do so or larger 'Cabals' for particular bigger 'Threats' (could be thought of as missions and campaigns).
Despite the wall of text above, this is a brief and thus scant explanation. For those interested in the background that makes up WH40K, there are numerous books, web sites and Youtube videos on the subject that go far deeper into these subjects.
Hope this helps.
Edit: Removed several typos concerning '.