m2e-wtp configures dependencies following the maven scope rules :
- test : not deployed
- compile, runtime : deployed
- provided, system : not deployed
- optional dependencies are never deployed
So if you see a discrepancy between maven CLI and m2e-wtp, then m2e-wtp has a bug.
In this case, please open a bug report at [1] and attach a sample project reproducing the problem.
Generally speaking, workspace projects don't appear in the Projects tab of the build path dialog, but in the Libraries tab, under maven dependencies node.
The run on server option will only show you specific project types (web, ejb, ear, web fragments, ...)
As a rule of thumb, never ever use the deployment assembly page with Maven projects, as the settings will be overwritten with the next "update project configuration" invocation. It will also lead to deployment discrepancies between Maven CLI and m2e-wtp. Your pic shows src/main/webapp/WEB-INF/ being deployed to WEB-INF/classes, which is wrong. You should really delete that entry.
Fred