Thank you for your post.
Each Window you open allows you to perform separate finds. That way, you can keep your current record, open a new window, do some searching, and then return to the original window.
One option is to use a global field pop-up, take the value and perform a Find on the original window. One way to do this is to create two separate scripts:
Set Field [ <global field> ; "" ]
New Window 
Show/Hide Status Area [ Hide ]
Go to Layout [ <layout that only contains global field> ]
Move/Resize Window [ Current Window ; Height: 200 ; Width: 300 ; Top: 200 ; Left: 200 ]
This script sets the global field to null (to start a new search), opens a new window, hides the status area, goes to a layout that only displays the Global field and sizes it to a smaller size. Set the Global field to a pop-up with the value list "Lions, Tigers and Bears"; the same as your other field.
On this new Layout, also have a button to execute a script that takes the value from the global field and finds the records. For example,
Close Window [ Current Window ]
If [ IsEmpty ( <global field> )
Set Variable [ $var ; Value: <global field> ]
Enter Find Mode 
Set Field [ <your pop-up field> ; $var ]
Perform Find 
This script closes the current window. Since we entered the information into a Global field, its contents will be available in all windows. Therefore, we check to make sure an entry was selected. If not, we halt the script and you are left off where you originally started. Otherwise, we put the contents of the global field into a variable $var, enter Find mode, put the variable into the pop-up field and perform a find. For example, if you had selected "Tigers" from the pop-up, you will now only see the Tiger records.
Let me know if you need clarification for any of the above steps.
If you download this file: You'll get a demo file that pops up several such floating windows--including one for Find and also Modify Find. The scripts they use are a bit more sophisticated than the above example by TSGal, the scripts use an infinite loop to make sure the floating window stays at the front and keeps the user from interacting with any other windows until they either perform the find or close the window. There's also data being passed as script parameters from the buttons being clicked. That's how the same script can do either a Find or a Modify FInd.
The script also checks to see if this is a windows platform and takes steps to minimize the window resize issues that can take place on a Windows system with this type of script.
Be sure to examine the loop part of the script and make sure you have a button that uses halt script to interrupt this loop or you can get trapped with the find window up and no way to do anything else until you force quit FileMaker.