Where are maven plugins stored? in the local repository as well?
Yes. Plugins are downloaded from a remote repository and stored in the local repository. The exact final location will thus depend on the groupId of the plugins (the core plugins end up in ~/.m2/repository/org/apache/maven/plugins where ~/ stands for your home directory for example in windows server 2016 it is stored under this path C:\Users\YourUserName\.m2)
what happens if you build your application with eclipse?
Hmm… Nothing special.
Does it store the plugins inside the eclipse/plugins folder or still in the local repository?
No, Maven (embedded or external) uses the location defined in the <localRepository> element of the global or user settings (which defaults to ~/.m2/repository), unless you overrode the Local Repository path in Window > Preferences > Maven > User Settings.