Question: What I need is to clearly differentiate between the attachments (this is an approval, this is an offer, this is a PO, etc).
Is this possible, or it is working only in bulk (attach all files together)?

Thanks,

Answer: 
SharePoint does not support attachment metadata. I would suggest storing the attachments in a document library (probably with Content Types for Approval, Offer, PO, etc) with a lookup column to the associated item in your list.
You could create separate lists for each item requiring an attachment, then link those lists in a master table.