According to the Cochrane Handbook for Systematic Reviews of Interventions, a systematic review "attempts to collate all empirical evidence that fits pre-specified eligibility criteria in order to answer a specific research question. It uses explicit, systematic methods that are selected with a view to minimizing bias, thus providing more reliable findings from which conclusions can be drawn and decisions made."
Meta-analyses
A meta-analysis is a systematic review combined with is the statistical combination of results from two or more primary studies, typically by calculating a weighted average of the effect estimates from different studies.
Other review types
In addition to systematic reviews, there are many other review types, including:
Narrative review: does not employ a systematic search and study selection process, does not formally evaluate study quality
Scoping review: assesses the size and scope of available literature on a certain topic rather than attempting to answer a specific research question, does not formally evaluate study quality
Umbrella review: a review of reviews, compiles evidence from multiple reviews into one article
Your library: check with librarians at your institutions to see if they can serve as consultants or collaborators. Systematic reviews with librarian co-authors are associated with higher-quality search strategies.