To move information from FamilySearch to Ancestry usually requires 3rd party software where you download a Gedcom from FS and then upload to Ancestry. Also 3rd party software have different ways to compare info between the info on your computer database in the software and Ancestry or Familysearch using different sync functions. You should look at the variety of softwares to see if one has the functions you want. I find my software very helpful.
Thank you yes I am a church member
Then look for the tree symbol up on the bar to the left of your name in Ancestry and you can compare people between FamilySearch and Ancestry
Yes I am aware of the green tree, it was just about moving a lot of names in one go. Thank you for your help you have been great
Yes you have the ability to transfer linked "chunks" of the FSFT into a tree of your own making in Ancestry. You can also establish links between a single record in one of your Ancestry.com trees with the matching record in the FSFT for monitoring and comparison purposes.
In either event, the links allow you to update one record at a time via sync'ing. But the easiest way to INITIALLY get all of the FSFT data into your Ancestry.com account is to create a new tree there where you can pull those complete "chunks" of the FSFT over into.
I can't remember what the limit is but if I remember correctly, it was like 4 or 5 generations at a time. But you can build the Ancestry tree by doing multiple transfers.
There are ways to download large portions of your tree using 3rd part software
and then creating a GEDCOM from that - and then uploading that GEDCOM to Ancestry
You said "family History" - I am referring to the actual data of names and relationship and events in FamilySearch Family Tree. the use of the word "family history" in your questions is a bit ambiguous as to what it includes.