Share permissions are nearly pointless. A share is like a doorway to the disk. Shares only allow you to control permissions on that one doorway.
NTFS is the file system used in Windows. It allows permissions to apply to each and every file and folder.
When evaluating permissions, Windows uses the MOST RESTRICTIVE permissions. Meaning, if the share says EVERYONE: Full Control but the NTFS Security says EVERYONE: Read Only, then everyone has read only and vice versa.
Because NTFS permissions can be granularly applied to files and folders and share permissions ONLY apply to the share, I usually IGNORE share permissions, setting them to EVERYONE FULL and then assigning NTFS permissions (Security Tab).