Almost all analog 'scope display slightly behind real-time...perhaps by 50 to 100 ns.
Digital 'scopes likely add much more delay....
Waveform samples collected in real-time are often stored in digital memory. From there, a microcontroller transforms samples to drive the digital display. The microcontroller may be required to do other calculations (for example: calculate mean voltage, RMS voltage, peak voltage, frequency) that slows display.
Depending on processor speed and display interface, you cannot know the display latency. Samples stored in memory can sit undisplayed for a very long time.
For example, my digital 'scope states that up to 2000 waveforms per second can be displayed, if no additional waveform calculations are requested. No mention is made of display latency, which is an entirely different matter.
If a 'scope user must discover timing relationship between two events, use a multichannel 'scope, or one with an independent trigger input. The timing between a trigger event, and a displayed waveform is available to the user, with a decently defined specification in the manual. Similarly, timing between channels of a multichannel 'scope is well-defined.