I am not sure I understand what you mean by live TV; I assume you mean the buffer. The buffer is main memory (or reserved disk space memory) that keeps 30 minutes of the show, right? As far as the software is concerned there is very little difference between a recording in the buffer and a permanent recording. Trick Play might be something special but I do not see an explanation here that makes it special.But with a DVR, you can do those things without recording - to live TV. It's why one of the "magic" features has been to "pause live TV".
Perhaps not for DVRs but there are many applications, such as VLC, that allow us to jump around within a recording.And I know my DirecTV Genie is tolerable, even decent, certainly better than nothing, but not at all up to the high bar that TiVo has set. But in both cases, I'm not sure there is a discernable difference in trick play functionality between live and recording.