To help decide whether to make these synonyms I recommend visiting the Leaflet home page rather than the tag wikis you linked to, because the result of this discussion may warrant revising the wiki(s) of the surviving tag(s).
The other thing that helps determine usefulness of tags is how often they are used and how easily they are to apply accurately. These links will let you quickly review that:
I will defer to those who use Leaflet rather than give my opinion on whether these should be made synonyms.
I am a strong believer that there is more to a library of functions than just its API.
Specifically, there may be ask-able (and answerable) questions regarding the history of leaflet, its support structure(s), and the use of plug-ins and extensions distinct from the API.
That being said, the question becomes whether StackExchange will generate improved community response from a single tag (which is what identifying these two objects as synonyms will effectively enforce) or whether the community will react/behave/respond differently to API-based questions as distinct from general Leaflet questions. -- My answer is that combining and simplifying the tags will likely draw increased community support for the conversation surrounding leaflet and its API.
As noted above, most leaflet-api questions have both tags already, so the community has already combined their tags by [mostly] using them together. I found only three community questions where 'leaflet-api' was tagged without also tagging 'leaflet'.
Hope this helps moderate/manage the StackExchange meta.