Oscilloscope coupling and effects on the measured signal
The signal generator has an output impedance of 50\$\Omega\$, so connecting it to an oscilloscope input with 50\$\Omega\$ impedance gives you half the the signal across the input. Your signal generator may have a 50\$\Omega\$ output impedance selection that does not really change the output impedance but delivers double the set amplitude in anticipation of a 50\$\Omega\$-terminated load, when that option is selected. 

Normally you will want to use high impedance (usually with a 10x probe) on your oscilloscope in order not to disturb the signals. The 10x probe will give you 1/10 the loading on the signal. You will also normally want to use DC coupling. AC is useful when you want to look at a small signal on top of a large DC bias (for example, ripple on a power supply). When set to AC coupling, the average value of the signal becomes zero, so a small duty cycle positive-going pulse will be slightly below zero when low and well above zero when high. 

You would use the 50\$\Omega\$ scope input primarily for high-frequency signals where you are dealing with a source that is intended to be terminated with 50 ohms (and you would use 50\$\Omega\$ coaxial cable to transmit the signal, usually with BNC connectors on most oscilloscopes). 

You may wish to use x1 probes when your signal is small in relation to the noise floor of your oscilloscope and you can tolerate the additional loading (typically some tens of pF and 1M\$\Omega\$).