Function generator outputs
Think of the function generator as a Thevenin source.  If you don't know what that is, look it up since it's well worth learning.  In fact, look up Norton source too.  Thevenin and Norton sources are two sides of the same coin.

Briefly, you can think of your function generator as a ideal voltage source with a resistance in series.  That may not be how it is actually constructed, but the point is you can't tell the difference from outside.  This means that if you measure the open circuit voltage of a signal the function generator is producing on the 50 &Omega; output, then connect a 50 &Omega; load to it, the voltage will drop to half the original value.

If you connect a 1 k&Omega; load to the 50 &Omega; output, then you have a voltage divider with the top resistor 50 &Omega; and the bottom 1 k&Omega;.  This means the output voltage will be (1 k&Omega;)/(50 &Omega; + 1 k&Omega;) = 0.95 of the open circuit voltage.

The reason 50 &Omega; and 600 &Omega; were probably chosen is because 50 &Omega; is a common impedance for tranmission lines, like some coax and twisted pair ethernet.  600 &Omega; is common in audio applications.