What are presynaptic puncta? And what makes them different from presynaptic terminals?
I found another article (Ippolito & Eroglu, 2010) in which the authors do explicitly clarify their use of the word puncta. In this article, puncta is a term used in the Puncta Analyzer plugin for ImageJ. Image J is freeware to analyze histological preparations and features many options for histological analyses. ImageJ was also used in the article you originally referred to (Molofsky et al., 2014). The plugin specifically analyzes co-localizing spots identified in a preparation. Co-localization can be studied by, e.g., labeling of two different antigens (double-labeling). Co-localizing fluorescent markers in a preparation often indicate that the two proteins are localized very closely in the cell, and are probably involved in the same mechanism.
To extrapolate the information back to your question we could formulate a hypothetical histological example involving neurotransmission. Presynaptic puncta could then be formed when (e.g. red) fluorescent antibodies for an autoreceptor and another (e.g. green) fluoresecent antibody targeting a modulator of the autoreceptor would colocalize on a presynaptic membrane of a certain synapse. The green and red would appear as a purple spot in the overlaid image, and the plugin would identify this as puncta, in turn showing that the two are very close in the synapse on the presynaptic membrane.
In all, given the heterogeneity of the articles reviewed and their use of the term puncta, I think 'puncta' can be loosely defined as: "(immuno-)histological locations defined by computer algorithms using ImageJ and related plugins".