Internal pull-up are generaly used to have a known state on inputs, even if the input pin is left unconnected.
Open drain is related to output, but need to be connected to a pull-up for correct operation.
Open drain outputs can be connected together or can be connected internaly to an input. This generaly the case on I/O port pins. The port, or pin direction (input or output) is selected through an internal register.
The pull-up can result in large leakage current .
Therefore it need some kind of weak pull-up instead .
It is usually implemented by pmos and change a lot from process variation .
The I/O pads can be characterized according to their Pull-up or Pull-down resistor values which may range between 25kOhm and 100kOhm. Therefore the distinction between a weak pull-up/down and a large one is dependent on the designers perspective.