Question: In the Harry Potter books, Diffindo is called the 'Severing Charm' and it’s most commonly used to cut ropes and the like. However, in the last book Hermione uses it on Ron but misses, creating a 'slash in his jeans' and his knee gets cut, causing him to 'roar in pain'.

We've only seen Sectumsempra used once on screen when Harry directly uses it on Malfoy in the sixth book, but there it's mentioned that he is 'waving his wand wildly'. Wouldn't Diffindo, if used in such a fashion also cause a similar effect? Similarly, if it was able to cut Ron, it would also be able to, say, chop off an ear (George's)? 

In that case, how are these two spells different, except for Sectumsempra seemingly used exclusively to hurt humans?

Answer: 
Sectumsempra can't be healed in the normal way, because it is "Dark magic", as we see when George's ear was cut off.
Sectumsempra is just more powerful.
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I found an interesting Quora post on this and it seems relevant enough so here goes...

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> Sectumsempra is extremely similar to a severing charm named Diffindo. Here's it's description.
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> > With the Severing Charm, cutting or tearing objects is a simple matter of wand control. The spell can be quite precise in skilled hands, and the Severing Charm is widely used in a variety of wizarding trades. Useful as it is, this charm should be practiced with caution, as a careless swipe of the wand can cause injury.
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> Which is extremely similar to what we know of Sectumsempra and it's after-effects.
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> > Blood spurted from Malfoy's face and chest as though he had been slashed with an invisible sword. He staggered backward and collapsed onto the waterlogged floor with a great splash, his wand falling from his limp right hand. Slipping and staggering, Harry got to his feet and plunged toward Malfoy, whose face was now shining scarlet, his white hands scrabbling at his blood-soaked chest.
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> (It should also be noted that the power of Sectumsempra can be controlled. When Severus used it on James, it only resulted in a little gash on his cheek, while Harry's wild cast almost resulted in Draco's death.)
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> Though the two are quite similar, they do have a few differences
> Sectumsempra is a curse, classified as dark magic, while Diffindo is a charm.
> Organs severed with Sectumsempra cannot be grown back. Those severed by Diffindo probably can
> They both have different wand movements.  
> *- [How did Snape invent the Sectumsempra in “Harry Potter”? - Quora](https://www.quora.com/How-did-Snape-invent-the-Sectumsempra-in-%E2%80%9CHarry-Potter%E2%80%9D)*
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The post goes on to speculate that Snape perfected the Diffindo charm from "a charm used for cutting herbs" into "a curse capable of cutting through human flesh". So, from this we can see that Sectumsempra is (in essence) a refined Diffindo.