Q: If two people use one computer, but we have separte itunes accounts, Apple ID, and icloud will my apps I get be stored in their account too since we are using the same computer?

If you  have separate user accounts on the computer, then your downloaded apps are stored in your iTunes Library. See the following for dealing with having multiple users on the same computer: How to use multiple iPhone, iPad, or iPod devices with one computer.

Using More than One iDevice on the Same Computer

This applies mainly to couples who are adding another device and do not want their email, messages, etc. being duplicated on both devices. To begin read: How to use multiple iPhone, iPad, or iPod devices with one computer. You need to establish a separate Apple ID and password for whomever will use the new iDevice. See Apple - My Apple ID and Frequently asked questions about Apple ID. The easiest way is to do this on the computer using iTunes: iTunes- How to set up an Apple ID within iTunes.

On the computer create a new user account for the person with the new iDevice. This will be the user account that person will always use. He/She will no longer use the other user account. This way that person will have a separate iTunes Library

Start by transferring the new device(s) to a new account along with all your data.  Save any photo stream photos that you want to keep to your camera roll (unless they are already in the camera roll) by opening your Photos app, tap on Albums icon at the bottom. Now, tap on My Photo Stream album; tap Select; tap on the photos you want to select;, tap the share icon (box with upward facing arrow) in the lower left corner; then tap Save to Camera Roll.

If you are syncing notes with iCloud that you want to keep then you need to open each of your notes and email them to yourself. Later you can copy and paste the text into new notes created in your new account.

Tap on Settings > iCloud > Delete Account (only deletes it from this device, not from iCloud; the person keeping the current account will not be affected,) provide the password to turn off Find My Phone and choose Keep on My iDevice when prompted.  Sign in with a different Apple ID to create your new account. Choose Merge to upload your data.

Once you are on separate accounts, you can each go to icloud.com and delete the other person's data from your account.

Note: The essence of the above was created by user, randers4. I

have made substantial changes to improve readability and syntax.

That is right. You are all using the same iTunes Library. You may configure your devices separately in terms of what you sync from the iTunes Library, but you are not separate otherwise. Only one Apple ID can be associated with an iTunes Library. Everything you've downloaded will show up for everyone else using the same iTunes Library and signing in with the same Apple ID.

That's your iTunes Store account. I'm talking about the iTunes Library on your computer that all the devices use when they sync to the computer.

If you are all purchasing stuff using your own Apple ID and iTunes Store account, then you should all be using your own separate user accounts on the computer.