The iPhone maintains two separate Apple IDs: one for iCloud, and one for the iTunes Store. These may or may not be the same, and they are set in two separate places.
To view and set the Store account, open Settings and scroll down to Store. Beneath the settings for Automatic Downloads, it should show the Apple ID you're currently using on the phone for the Store, e.g.:
Apple ID: pito@mac.com
Tap that, and a dialog will pop up offering three options: View Apple ID, Sign Out, and iForgot (the last is for retrieving a forgotten password).
If the Apple ID displayed there is not what you expect, select Sign Out, and you will be able to sign into the Store with a different Apple ID. Note that this will not affect your iCloud settings, which are managed separately through Settings > iCloud.
Give this a try, and if you are still having troubles, feel free to update your question.
Further note: it sounds like you have inadvertently set up a new Apple ID instead of using an existing one. To identify which Apple IDs are associated with your account, check out My Apple ID. The Manage Your Account and "Not sure if you have an ID? Find out" links should help you get a handle on the situation.
Update: Regarding your comment about the App Stores, there's definitely confusion to be had here: The "App Store" on iOS is part of the iTunes Store - it's the same content that you see when you open iTunes, go to the Store, and browse to Apps, and it uses the same iTunes Account. The Mac App Store, accessed by clicking the App Store icon in your Dock (or under the Apple menu) in OS X is a separate content store containing only OS X apps. That said, it also authenticates using an iTunes Store account, typically the same one you'll use in iTunes.
As of today, the easiest way I've found to think about this - and the way I've configured my own accounts - is:
An Apple ID for buying things, which you'll use to authenticate in:
- The iTunes Store
- The App Store on iOS
- The Mac App Store on OS X
And one for syncing things, which you'll use to authenticate in:
- The iCloud settings on iOS
- The iCloud preference pane on OS X
- The iCloud website
The thing to note about the above is that you can use the same Apple ID for both sets of tasks, but, depending on what you want to accomplish, knowing where to enter each ID is important.
When you install Apps, you usually install them to the Applications Folder, which is accessible to all users, because it is in the ROOT directory, not just the users that installed them. You can create an Applications Folder in a User's Folder and keep them for just that user, but it usually is the first way I mentioned. That way when you make a new user on the fly, you don't have to install all those apps again, waisting space. Also, that way you don't lose apps that may have taken time to install that other users need and use.
Applications that are installed to a computer through the App Store are linked to an Apple ID that was used to Purchase/Download it. This is similar to iOS devices as well. If I download an app on another persons iPhone using my account, they need my account to update it.
So this means one of two things:
Either your wife bought iPhoto (Or which ever other App is in question) or when you bought the computer, registered iPhoto to her account.
When you buy a new mac, it comes with iLife, and iLife is now downloaded through the App Store. It will link those 3 Apps, to the Apple ID of your choosing so that if anything happens and you need to do a restore or something, you can download those apps you got for free again, no problem.
I had to do this when I bought my mid 2011 Mac Mini.
So she either purchased it or registered it to her account, and that is why it is still on the computer, because it is an App that can be accessed by any user that is on the machine, so it wouldn't have been deleted when she installed it/registered it. You will need her sign in and password in order to update it.
I hope that this information helps you out.
Best Answer
Strictly speaking, the cloud/arrow button is the install button. You are missing buttons to acquire the app and add it to your account (either GET or PURCHASE).
Try signing out of your iTunes Store account, restarting your phone (power off and on), and sign back into your iTunes Store account. That cloud button should still appear and allow you to add the app to your phone (it should turn into a loading spinner, and then an OPEN button).