People really seem to struggle to realise how different they are. Hamas is not ISIS, that should be obvious to anyone with cursory knowledge on the history of the region. Hamas, Hezbollah and Ansar’Allah are not going to, nor have the capacity to, gut gay people and women who don’t wear a niqab or hijab. They are not Salafists, for the love of Christ.
The only reason people compare these wildly different groups, is because they all (at least claim to) adhere to Islamic principles. If you think for even a second, you’d realise how ridiculous this is. It’s like comparing the CDU to the KKK or even the Spanish Falange because they’re all Christian, in some way or another.
It’s plain ridiculous, though the liberal (and conservative) types never seem to get it.
Without a detailed graph of all of the policies, actions and history of each organization so you can compare and contrast them all, and the willingness for each person to study that graph, there is no way to get people to know the difference.
Most people don’t know the difference between the United Kingdom, the British Isles, England, Great Britain, Ireland and the Crown Dependencies are, or what all of the different subdenominations of Christianity are, as you mentioned. Without a large degree of interest in learning what the differences are, or a high level of pertinence to someone’s life, educating them to the differences and similarities would be next to impossible.
The best you could probably do is have a one-sentence summary of what each group is all about, and hope that your audience doesn’t immediately discount it based on what they think they know about that group. For example, “Hamas: Their unifying tenet is armed resistance to Israeli occupation of Palestine”. If the general sentiment towards Hamas by the West is anything to go by, your audience would probably question even that. If it was easy, it would have been done already.
It’s an uphill battle.