In linguistics, diachrony refers to the description of a language as it changes through time, as opposed to synchrony, which only looks at one moment in time. One could consider diachrony the study of language change (overlapping or even synonymous with historical linguistics).
The process of taking a language and applying the kinds of changes found in natural languages is commonly done by conlangers and is called diachronic conlanging, or colloquially doing diachronics.
The question has now come up about the appropriate tags. It has been suggested to use diachronics specifically for diachronic conlanging, in contrast with language-change for whatever other questions may come up regarding the natural change of language. Most of these questions would likely be related to diachronic conlanging anyway (basically any question asked here about how certain changes work, what changes are common, whether certain changes are attested… would be asked with diachronic conlanging in mind), but there might be some interesting questions about how conlangs have changed in the hands (or mouths) of actual users, for which language-change might be more appropriate.
Personally, I don’t really see a need to differentiate in the use of these two tags and would consider them synonyms. If we do not wish to consider them synonymous, I’d like to develop good tag descriptions here.