If you manually enter find mode and type in the same company name into this companies field, can you find the expected records that way?
Is companies a field of type number or type text?
In layout mode, do you see ::companies as the field name or companies (no ::)? If you see ::companies, this could be why as this indicates that Companies comes from a related table. When you specify find criteria in a field from a related table you are telling fileMaker to "find all records in the layout's table that have at least one related record matching this criteria." Thus, the record you are getting may have more than one related record and it is another, not visible related record, that is matching your company name criteria.
On a form layout, native to its table. There are no related fields relevant to this thread.
Company is a text field.
It works fine when I do a manual find.
Very frustrating. What am I doing wrong?
Do you have
Perform Find [restore] ?
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I had [Restore]. Made that go away, and it works now.
Except -- the script goes to CompanyID instead of Company. Have to manually tab to Company.
Go to Field [Companies::Company] *** The form is based on the Companies table.
Perform Find 
Really what I'd like is to hit a button, have a field come up to Company and just type any desired text. I'm short-cutting around that as it seems prohibitive to accomplish right now.
Do it this way:
enter find mode  //no pause
go to field
pause /resume [indefinitely]
See why that works?
Yup, it works great.
Except you have to hit Enter twice, but that's being *waaaay* too picky.
I like that it goes back to Show All.
I personally don't set up scripted finds like in this manner. It's so similar to how the user can do their own ad hoc finds (the bane and boon of Filemaker database interface design...), that I don't bother to make the effort.
If I find that I need to provide scripted support for searching the database, as is often the case, I use a script that uses new window to pop open a small floating window that simulates a modal dialog. The user specifies criteria in global fields in this window and then clicks a button to close the window and perform the find. The script performed by this button click then uses the data in the global fields (Data in global fields can be accessed while in find mode), to build the needed find request(s) and performs the find.
This approach allows me to set up interface details customized to specifying find criteria such as drop down lists with trigger controlled scripts and field validation rules in place to catch obviously invalid find criteria before the user attempts the find. I've even added a calculation field that uses the criteria entered to contstruct a plain language description of what the find will produce to help the user understand what they'll get.
You can see an example of this method in the Known Bugs List Database that I created and maintain on behalf of this forum.