Ubuntu Software says there are updates while Software Updater says there are none

Steps:

1) Clean install Ubuntu 16.04 Desktop x86 64
2) Run Software Updater and install all updates.
3) Restart.
4) Run Software Updater again and observe there are no updates.
5) Run Ubuntu Software and observer there are updates.
6) Install the updates.

Expected:

Both update methods would have the same result, or one of them should not be installed by default.

ProblemType: Bug
DistroRelease: Ubuntu 16.04
Package: gnome-software 3.20.1+git20160426.1.a976144-ubuntu-xenial-0ubuntu1
ProcVersionSignature: Ubuntu 4.4.0-22.40-generic 4.4.8
Uname: Linux 4.4.0-22-generic x86_64
ApportVersion: 2.20.1-0ubuntu2.1
Architecture: amd64
CurrentDesktop: Unity
Date: Fri Jun 3 12:37:15 2016
ExecutablePath: /usr/bin/gnome-software
InstallationDate: Installed on 2016-06-03 (0 days ago)
InstallationMedia: Ubuntu 16.04 LTS "Xenial Xerus" - Release amd64 (20160420.1)
ProcEnviron:
 LANGUAGE=en_GB:en
 PATH=(custom, no user)
 XDG_RUNTIME_DIR=<set>
 LANG=en_GB.UTF-8
 SHELL=/bin/bash
SourcePackage: gnome-software
UpgradeStatus: No upgrade log present (probably fresh install)