Were your blueberries grainy? I occasionally get a pint that have a grainy texture. I've heard that this means they aren't quite fresh, but they usually taste just fine despite the texture. I'm not sure if this particular graininess translates to a jam though.
Jam can also get grainy from sugar that isn't fully dissolved. This can happen more easily with larger batches, since the fruit can start to boil before the sugar is fully dissolved.
For your particular recipe, perhaps a more thorough stirring after adding the sugar would help. You should be able to turn the heat down once you add the sugar so that you can stir it thoroughly before going back to high heat to boil for that 1 minute.
Common names of plants are a very unclear matter. There are big differences not only between languages, but also regional differences within a single language.
There are lots of (closely related) plants which are sold under the name blueberry. And probably not even the person who grew (or gathered) them can tell you the exact species. While it does matter when it comes to jam (for the same reason it matters whether you use Roma tomatoes or Cherry tomatoes for a sauce) it is highly improbable to find a source which can consistently provide you with a specific known variety. Also, you probably have to study some very specified botanical literature and be provided with parts of the plant other than the berries in order to be able to identify the type with some degree of accuracy.
On the other hand, don't let that come in the way of good jam. Blood orange marmelade may taste different than bitter orange marmelade, but both are good. The same goes for blueberries: you can use any variety, even if some of them would be a bit better on their own.
What you need for a jam is a good sweetness to acid ratio, the proper amount of pectin, and as much aroma as possible. A softer texture also helps to prevent unpleasant lumps. So generally, you want to go with the ripest fruit available. They are soft, and have the fullest aroma. This is something you might want to consider with your current source of berries: maybe they're not a special "green on the inside" variety, but only underripe. If they don't taste very sweet, and their aroma isn't very complex, I'd try to find other sources. Farmer's markets and organic stores are usually able to sell much better fruits (because they cater to a picky, price-inelastic clientelle), but of course they cost a lot too.
Sweet fruit is always good, but you need enough sugar added for food safety. A ratio of 2:1 (fruit to sugar) can still be kept in the pantry, more fruit than that and you need to refrigerate the unopened glasses too. With blueburries, you'll need to add both pectin (to get the jam to gel) and acid (to get the pectin to work). This is the part which will vary with fruit variety: more watery types will need more pectin, and less acidic types will need more acid. If you want a good quality jam, you'll need to do some experiments until you get the proportions right. If not, you can buy "jam sugar" or however it is called in your country - this is sugar with pectin and acid already added. It won't have the perfect ratio for your fruit, but it will more or less work. But then, if this quality is enough for you, you can skip buying the expensive berries and slaving at the stove, and buy manufactured jam.
Best Answer
Blueberries are generally low-pectin fruits, so many jam recipes and jam making guides specifically call for adding pectin. That said, some do not - but these use the whole pureed fruit. When you filter out the seeds and skin, you remove much of what pectin there is in blueberries naturally, leaving you with runny jam.
The solution, then, is to add pectin or some other fruit that contains some.
As a note, unripe fruit, including blueberries, often has more pectin than ripe, but if you're using frozen blueberries, they're likely to be picked at their peak and rather low in pectin.