I noticed that we have both tags. They are not synonyms and I cannot suggest them to be. However, their descriptions sound pretty similar:
Average weather conditions for a particular area measured over multiple years or decades. For questions on climate change use the climate-change tag.
In contrast to the short-term variable weather, climate describes the mean conditions of atmosphere. Thus it is the statistic of weather (mean values, extrema, etc.). Often a 30-year period is considered. When asking questions about climate, use this tag and also include the atmosphere tag.
Should we merge them?