Time terminology

• Calendar time is the time that has elapsed since the epoch (t - E).
• Local time is calendar time corrected for the timezone and DST.
• Wall time: I assume you mean wallclock time. This it the time elapsed since a process or job has started running.

RTFM time(7), localtime(3), time(1).

Epoch: Used to refer to the beginning of something. such as the Unix Epoch which is of 00:00 , January 1, 1970 UTC. (i.e. a time_t with the value 0 represents midnight, Jan 1. 1970 UTC)

calendar time: the time since the epoch

local time: the calendar time in the timezone you (or the computer) resides in.

wall time: time elapsed on a real clock since some arbitary start , e.g. since you started a program (as opposed to e.g. CPU time used by a program since it started)

Try info and then * Date input formats: (coreutils)Date input formats. which starts with this wonderful text:

Our units of temporal measurement, from seconds on up to months, are so complicated, asymmetrical and disjunctive so as to make coherent mental reckoning in time all but impossible. Indeed, had some tyrannical god contrived to enslave our minds to time, to make it all but impossible for us to escape subjection to sodden routines and unpleasant surprises, he could hardly have done better than handing down our present system. It is like a set of trapezoidal building blocks, with no vertical or horizontal surfaces, like a language in which the simplest thought demands ornate constructions, useless particles and lengthy circumlocutions. Unlike the more successful patterns of language and science, which enable us to face experience boldly or at least level-headedly, our system of temporal calculation silently and persistently encourages our terror of time.

... It is as though architects had to measure length in feet, width in meters and height in ells; as though basic instruction manuals demanded a knowledge of five different languages. It is no wonder then that we often look into our own immediate past or future, last Tuesday or a week from Sunday, with feelings of helpless confusion. ...

-- Robert Grudin, `Time and the Art of Living'.