Those two functionnalities are very similar since they use the corresponding Solr basic functionnalities that rely on a text file.
Unless it has been modified, those text files are located in the conf folder of the FileShare core.
Note that from a functionality perspective, the Admin UI proposes a html UI with forms to properly edit these files without directly accessing them.
In these Solr files, the syntax for the synonyms is as follows :
i-pod, i pod => ipod, sea biscuit, sea biscit => seabiscuit
The syntax for the stopwords file is the following one :
a an to from
To prevent two people from modifying the same text file at the same moment, the servlets dedicated to these functionnalities use a mutex semaphore. There is also a list_language.txt that you have to fill, which defines where to apply the semaphores.
You can see the effect of the stopword filter in the solr admin UI analysis.