Ecological and evolutionairy effects are sometimes difficult to distinguish.
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First, the setting for this question is almost always related to explaining some aspect of broadly defined trait differences in extant (currently-living) species. The specific problem at hand is one in which someone is trying to explain what may drive the observed differences among competitors. It is unclear whether such differences are relatively recent (ecological time) or old (evolutionary time).
Consequently, the phrase "invoking the ghost of competition past" implies that someone thinks the observed pattern of differences may have been caused by a process that took place a long time ago, and may not be presently observable/measurable. Anyone performing research on this topic would then have a comparably hard time ascribing causes of differences to ongoing competition, as opposed to past competition.