On a circuit board we are supposed to use for laborations there are circuits for D flip-flops that looks like this (this picture shows how the connections actually look at the circuit board, the square signs are where connections can be made):

Here CK = Clock, D is input and Q is output.

However when I searched the web I found pictures of D flip-flops that looked like this:

How are these pictures of D flip-flops related? CLK and CK are of course the same, CLEAR I guess is a way to reset the output value to zero and I assume D = J and Q = Q. But what then is K and Q-bar? How can one simplify a circuit that included K and Q-bar, so that it only uses D (J) and Q?

 

The second drawing is not a D-type flip-flop. That is a J-K flip-flop with CLEAR'.

Q and Q' are outputs. If you do not need to use Q' just leave it unconnected.
Some chips provide both Q and Q'. Others don't.

You really ought to search for a D-type flip-flop.
If you absolutely want to convert a J-K flip-flop to a D flip-flop, there is a way to do that. I leave that as an exercise for you.

 

An advantage of the JK Flip-flop is that it can do four different things:

Clear the Q output to 0. Q' goes to 1
Set the Q output to 1. Q' goes to 0
Toggle the Q outputs, which of course toggles the Q' output
Hold the present state aka 'do nothing'
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There is also the similar, but slightly different JK_BAR Flip-flop.

Now there are two types of designers: JK and non-JK. Which type do you want to be?