Wikipedia users, move protections, and move access
  Unregistered, New (Auto) confirmed Extended confirmed File mover Page mover Template editor Admin Appropriate for
No protection can edit
cannot move
can edit
can move

Most pages

Semi-protection:
edit=autoconfirmed
move=autoconfirmed
cannot edit
cannot move
can edit
can move

Unregistered/newuser vandalism / edit warring

30/500 protection:
edit=extendedconfirmed
move=extendedconfirmed
cannot edit
cannot move
can edit
can move

Areas authorized by the Arbitration Committee

Files (not a protection level) cannot move can move cannot move* cannot move can move

Files

Template protection:
edit=templateeditor
move=templateeditor
cannot edit
cannot move
cannot edit
cannot move**
can edit
can move

Highly-visible templates, modules, and other pages

Page mover protection??
move=pagemover
(edit undefined)
can edit?
cannot move
can edit?
can move**
can edit?
should not move***
can edit
can move

--

edit=pagemover
(invalid)
cannot edit
cannot move
can edit
can move
cannot edit
cannot move
can edit
can move

Should be invalid, but no way to enforce??

Move protection:
move=sysop
(edit undefined)
can edit?
cannot move****
can edit
can move

Move warring, or unlikely to require moving

Full protection:
edit=sysop
move=sysop
cannot edit
cannot move****
can edit
can move

Persistent vandalism / edit warring, and critically important templates and modules

*Page movers do not have movefile and hence should not be able to move files.
** If pagemover is implemented as a new protection level, pagemover should not be higher than templateeditorin protection hierarchy, because page movers may not meet template editor criteria.
*** If pagemover is implemented as a new protection level, templateeditor should not be higher than pagemover in protection hierarchy, because template editors may not meet page mover criteria.
**** MediaWiki backend does not support a page mover to be able to move a fully move protected page, and have that revoked when full edit protection is applied (I believe). Implementation may be possible, but it's very fussy and dicey.