I have a system that was designed for testing digital components.  I have a device in the system which is used for generation and acquisition of digital signals.  Now, I will happily admit to not fully understanding everything I'm about to say, but:


The outputs of the device have a 50Ω nominal impedance,
The cable carrying these signals is a 50Ω cable designed for the device,
The PCB the cable is plugged into is supposed to use 50Ω characteristic impedance on the lines with length matching to 0.5" and signals routed on the same layer.


For clarity:  the output of the device is sent through a cable, which is attached to a PCB, where the signals are routed a short distance to a high pin-count connector.  I am trying to see how high of a frequency I can reasonably generate with this device, so I started with the default for the software I have:  50MHz.  And the signal looked like this:



When I slowed down the signal to 1MHz to get a closer look at the transition, I got this:



I believe that I'm following the instructions in the device's specification sheet correctly...50Ω cable (designed for the device), 50Ω traces on the PCB (if the company who designed the PCB did what they said they did), into a high-impedance load (my scope).  

I suppose my question is this:  am I measuring the signal wrong, or was the system designed wrong?  Is there anything that I am grossly misunderstanding?  If the system was designed wrong, are these graphs sufficient to show that or is there another measurement that would be more illustrative?

Edit:  I was asked to show what the signal looks like when "properly" terminated, aka not just floating non-terminated out of the connector of my system.  The process through which this signal arrives is kind of a mess (see my comments) but here's what I've got:  



Edit#2:  I stuck a 50Ω resistor between the digital output I'm observing and the ground that the signal is referenced to and I got the following output.  From my understanding of this conversation, this seems to not be what I would have expected.  



Edit#3:  See The Photon's accepted answer, but here's what the signal looked like after I removed a long, unterminated cable that was essentially dangling in the wind and also terminated the point I was measuring with a 50Ω resistor.  



First: Yes, your understanding is essentially correct, other than the issue being voltage and not charge.

Here is my analogy:

Consider a door to a house, with really smooth hinges, and no bolt or latch. The door is so light and so well-hinged that the slightest breeze would cause it to flap open and closed.

Now add a light door-spring to the door. The spring keeps the door shut, but not terribly firmly: A gentle push will open it, and letting it go will cause the door to close again.

A so-called "floating input" is like that door - the slightest perturbations in  electromagnetic field, like the breeze above, will cause the input to randomly toggle between open and shut (low and high).

Add the pull-up resistor (if you want the default to be "high") or pull-down resistor (if you want it to be "low"), and your spring is in place. 

Now, an external voltage applied, like the gentle push, can overcome the "keep the door shut" tendency of the spring / pull-x resistor - and once the push is removed, the input returns to the desired default value.

A low value resistor in such use is like a really stiff spring - it needs a much firmer push to open, but open it will. It will also slam shut faster when the push is removed.
