Well, as wargammer55 pointed out, the battlecruiser is definietely an off-shoot of the dreadnought family tree. In the sense that they mounted an all-big gun armament, they were clearly a "dreadnought type" as far as that went. Not only that, but they sprang out of the same Royal Navy building programs and schools of thoght that created the Dreadnought.
The genesis of the "battle cruiser" as we think of it (a capital ship with a battleship armor yet high speed) was born out of Britain's strategic needs; at the turn of the 20th century, Britain had a far-flung empire and relied heavily on the merchant ship trade between those colonies and her home islands. That made the threat of commerce rading during wartime a very serious one indeed, and given the primitive nature of submarines and the "laws of war" that prohibited the surprise sinking of merchant ships, British naval thinkers concieved of the threat primarily as one of surface raiders, especially enemy cruisers. Even a handful of such raiders could do serious damage to a beligerent's merchant trade, which was bad enough. Even worse, their destruction and/or the protection of the threatened merchants tended to tie down an inordinate amount of resources, resources that could be "better spent" (in the eyes of most admirals) doing proper Navy things...like engaging the enemy's battleships in a decisive battle.
In order to catch these raiders, fast and powerfully armed ships would be needed, and hence the battlecruiser. At the most basic level, the British concept of a battlecruiser was a ship designed to be heavily armed and just well protected enough to chase down and destroy any cruiser-sized or smaller raiders, yet fast enough to run away from anything big enough (like another battlecruiser or a battleship) that could serioulsy threaten it. The fact that such a ship would also be a dangerous commerce raider in its own right was not lost on the navies of the world, either! In addition, it must be remembered that radar was still decades away, and both heavier and lighter than air aviation was in its infancy. Not only that, but radio communication was still very primitive, and not all that reliable. In that environment, the only way to find the enemy and bring him to action was to send out some of your own ships as scouts that would then have to spot the enemy fleet and report its discovery back to the main force, perhaps using signal flags! Considering that, one can see how a battlecruiser's speed would also make it a very effective scout.
In desiging the battlecruiser, the Royal Navy had to work within the constraints that the designer of any warship has to labor under, using the technology they had. All warships strike a balance between several cometing characteristics, primarily speed, armament, and protection. If the displacement (ie, the rough overall size of the ship) is held constant, then it becomes a zero-sum game; the designer can't increase the armament without reducing one of the other factors, like protection (armor) or speed. The only way to short-circuit this problem is to make the ship bigger (which adds difficulties of its own) or develop improved technologies that allow better performance in a given characteristic for the same (or even less!) size and weight. In the case of the battlecruiser, British naval archetects emphasized speed and firepower over protection, under the assumption that the resulting ship would be fast enough to run away from anything that could seriously threaten it. The resulting design was certainly fast for a capital ship of the time at 25 knots (a full 4 knots faster than the Dreadnought, which was herself several knots faster than any other battleship), and nearly as well armed with 8 12" guns to the Dreadnought's 10. However, her protection was far weaker; they were the classic "glass cannon," able to dish out horrible punishment but not able to really absorb it.
