For example: The Derffinger had a 300mm belt, the Kaiser a 350mm one. The Derffinger had 305mm guns, the Kaiser too. The Derffinger had 26.5 knots speed and the Kaiser slightly slower at 23.5. So why is the Derffinger called a battlecruiser then? I know that Kaiser Wilhelm II said that he wants his battlecruisers to have more armor than their British counterparts so that they can fight in the line of battle and counter Germanys numerical inferiority. And it worked great. But really, that meant that what makes a battlecruiser a battlecruiser, high speed and firepower but low armor, was not done. Rather they were nearly similar in stats to the dreadnoughts. So why were they considered battlecruisers?
I discussed this at length here. To summarise, the battlecruiser is best understood as a ship designed to fulfil a particular tactical role - acting as a heavy scout for the battlefleet before joining it to form a fast wing - rather than as a ship with a particular set of characteristics. The German ships, as ships designed to carry out the battlecruiser role, are battlecruisers.
An important note to better compare classes of battleship and battlecruiser is to if we must only compare them within their generation of ships. The definitions between nations are fluid at best and adapt with the capabilities of each new class.
Besides the very accurate doctrinal reasons fourthman lays down you are being undone by comparing ships funded and designed several years apart. The Kaisers are much closer to the Moltke's though the real partner battleship class for them coming off the design board was the Helgoland series. Here we see an ever more stark contrast in speed of nearly 7 knots when going all out on speed trials. Something that could be incredibly valuable when dictating the terms of an engagement with other light ships, and which Goeben demonstrated during her dash across the Mediterranean in August of 1914. The difference in main armament in clear too, the Helgolands have more and heavier guns than the Moltke's. Generally each battlecruiser class in both nations was ordered in conjunction with a battleship class, though often before the next battlecruiser class was ordered another battleship class would come too. The fleets wanted battlecruisers but they needed dreadnoughts, and then Super-Dreadnoughts, and by ordering by by 2's and 4's most often you could preserve each class tactically at sea or at worst with classes built within the same generation, and not be locked into a design for more than a few slipways and shipyards at a time.
But as each successive class of ships gets bigger stronger and faster yes newer battlecruiser classes at least on paper appear to catch up in guns and armor to older battleships. But due to generally being much larger in size the areas without as much armor are much larger and allow plenty of space to poke holes in for water or shells to enter.
And we see the same with the Royal Navy, the Admiral class of which Hood was the sole example has the same guns as the Queen Elizabeth and R classes, and as good or slightly more armor generally than the preceding Iron Duke class. But that doesnt make her a battleship, it just means that 4 years between laying QE's keel and Hood's that the willingness to build a ship big enough and propulsion systems were strong enough to squeeze high speed out of a ship that well armed and armored, it just was going to be hugely expensive and fuck all big. While she was still according to doctrine not going to operate with the main gun line, but in a scouting, screening, and flying cavalry role like her older battlecruiser cousins.