Context is key. To export just the related records, do it from a layout whose table occurrence references the table of records you want to export.
Do your find to find the section records. Then use Go To Related Records with the "match found set" option specified to pull up a found set of related records on a layout based on that related table. Now you have a found set that can be exported from FileMaker as a file or imported from if you want to import this data into a different FileMaker table (even if in another file).
Note that the Table occurrence that you specify for the layout where you produce the found set of records should be the table occurrence that you specify for importing or exporting the records.
I have a master inspection record and many related section records each in their own tables. There is only one matching section record for each inspection record.
Stopped reading here.