Real time means that the signal processing does not break the temporal continuity of the output signal e.g. a system acquire 1 ms of base band/ IF/ RF signal and produces as output 1 ms of output signal.
Signal processing takes part both in the analog and digital domain: the analog processing is mainly characterized by a delay but the temporal continuity of the signal produced is never compromised: it is inherently a real time processing because it consists of a transformation of the signal while crossing one or more cascaded analog stages.
When we consider digital signal processing we have to face other problems because this type of processing is achieved by a cascade of A/D conversion, DSP and then D/A conversion stages (if required): while the A/D and D/A (usually) are not a problem the DSP stage is implemented by software/firmware running on a processor (ASIC/FPGA/GPP or DSP) and requires time to complete its tasks according to the complexity of the operations involved, therefore the DSP stage is not able to process a new frame coming from the A/D until the current frame has been processed and sent to the D/A: this is the real time constrain that a digital signal processing system has to satisfy. If this constrain is not fulfilled the temporal continuity of the output signal is not granted.
For what concerns the on line processing I can't give you any suggestion because I never heard that expression before but I suppose that it is a synonym of real time. Maybe if you clarify the context where you find this expression it would be helpfull.
Regards
Mowgli