How to read system requirements & compare GPUs?
Unfortunately there isn't really a concrete way to look at models numbers and know how they will perform or which is better. Model names are arbitrary and naming schemes may change from time to time. However, manufacturers have some incentive to have at least some kind of coherent naming scheme at any given time for marketing purposes. If you want to compare specifications of a particular card (for example: your own graphics card) vs the required or recommended specification you can look up both at the manufacturer's website and attempt to make an informed decision. Also note that 3rd party services and benchmarks are usually available that will give you a moderately accurate numeric representation of the graphic cards' performance. A third alternative would be to search the internet and see if anyone is running that particular game on either the same or similar hardware.
Generally, you can check either the manufacturer's website or a retailer to try and glean information on the naming scheme. In the Nvidia example GTX 650 vs a GeForce 840M. You'll probably be able to note that the "naked" GeForce branding in general isn't as powerful as "GeForce GTX" and that the "M" stands for mobile and will generally be lower performance and feature limited but also require less power. To go into specifics the first number is (for example: the 6 in 650) generally denotes the generation of card and the following numbers will normally donate the intended performance.
So to give some full examples, a GTX650 compared to a GTX750 will likely be very similar in terms of performance. The 750 may run cooler, require less power or have additional features but any difference in actual performance will be at best marginal assuming that the manufacturer didn't change their naming scheme. Another example I can give that will be more illustrative would be a GTX 590 vs a GTX 960. The 960 is much newer, has more features and so on but isn't close to the performance of the 590 (despite being a much bigger number!). However, it's worth noting that with such a large timeframe between the two cards, the gap between the performance of an old "X90" and a new "X60" will slowly close due to improvements in technology, manufacturing, and to a minor extent developers targeting and testing with newer graphics cards.
As I said earlier, it's mostly arbitrary and Nvidia have changed their naming scheme between the 7600 GT and the GTX 650. AMD also have their own naming schemes that they can change too (and they are likely to differ from Nvidia's at any given time). Your best chance at a general rule is to check a 3rd party website and hope that they are accurate. The example given in your post could be checked on a website like this.
Developer hardware recommendations are sometimes inaccurate. However, from that information it looks like you should be able to play it on lower settings but YMMV.
Apart from the above mentioned options, there are two other ways to help distinguish between two cards, and ultimately, a much more effective way to determine if the game can run on your system:
Direct X Compliance
Direct X is an interface designed to make it easier to speak directly with the graphics card. It is a popular means to 'standardise' the graphics; in complete contrast, early games would actually list all supported cards, and you would have to read through and confirm that your card was directly listed.
If a game lists itself as requiring a "Direct X 10 compatible card", you must have a card that supports Direct X 10, at the very least. Even if your card outperforms the physical requirements, Direct X sort of becomes the language, and earlier cards simply would not understand everything the game attempts to do.
"Let me google that for you"
It surprises me how informative a google search can be, on matters of graphic card support. I always use the format of "(card one) vs (card two)", and am always met with some good comparative statistics from trustworthy sites.
Most of the time, the comparison is detailed enough for me to understand if one card would outperform the other card. I can see how the layman might still find the information confusing, so this comes down to how well you understand graphics cards and the physical requirements behind gaming.
In this particular case, the first hit is a comparison made by UserBenchmark.com. In this case, your card outperforms the required card in all tests. The site even goes as far as commenting on what each performance test implys;
For example, your card outperforms the required card in lighting by approximately 500%. UserBenchmark defines this improvement as "Hugely better.. peak lighting effects, peak reflection handling, regular lighting effects and regular reflection handling". In this particular case, this tells us that your card should be able to handle the lighting effects of the game, and can probably handle lighting at a much higher level of detail, if you have the option of upgrading the lighting quality through the video options.
Try it for yourself
This is the best way to see if your system can handle the game. Try it out, for yourself. Either way, your system should handle it, or not. You won't blow up your card by trying to run a game that requires a faster unit unless you try really hard.
This can be difficult, depending on the game; Game demos are your friend. If a friend has a copy they can lend or give access to, even better.
In the case of Heroes of the Storm; the game is free to play. Try it out, it should run. If it does not, it is not like you have spend money on a game you can not play.