Difference in Size of SQL Server 2008 R2 backup on Local disk and on Remote Network Share
You say you are "using SQLDATABACKUPANDFTP Software" if this software is from http://sqlbackupandftp.com/ then it says it "Zips, Encrypts and FTPs the database backups" which would explain much of the difference.

I'm afraid your screenshots didn't appear so I can't comment on the other difference.