I have a few ETL scripts I built using Talend Open Studio to move data over.
Using a tool like Talend (which is Free and has SFDC Connectors) or Informatica Cloud or Boomi, you can create scripts to pull data from your Production Org and populate in your Sandbox Org. Of course depending on your sandbox you'll hit size limits so you need to filter your data pulls. Not a big deal.
This approach also requires Enterprise Edition as you will need API access.
You can build your scripts to properly create the relationships.
For Example:
Step 1 - Upsert Accounts (Store SFDC Production ID in an External Field, say "PROD_ID__c".
Step 2 - Upsert Contacts (Store SFDC Production ID in an Exteral Field, say "PROD_ID__C". Use ACCOUNTID on the Contact as the External ID in the script to automatically relate the Parent / Child Objects.
Step 3 - Continue Pattern.
Pros of ETL Approach:
Repeatable & Saves you TONS of time on Sandbox Refreshes.
Less error prone as your not manually running Data Loader / Reports.
Low Cost if you use Open Source or Jitterbit, etc.
You can automate this to keep data in sync as necessary via schedulable services (Apple Automater, Windwos Schedule Services, etc)
Cons:
Requires some up front time & effort to build out the ETL scripts.
IF you modify the Fields in Production you need to update in Sandbox.
You need to know your Data Model. May sound stupid but if you have dependencies on multiple objects you need to build your script so that it loads the Object Records in an order that makes sense.
This is mentioned here in Sandbox Setup Tips and Considerations, specifically:
Sandbox copy is a long-running operation that occurs in the background. You are notified of the completion of a sandbox copy via email. Sandbox refreshes might complete in minutes, days, or even more than a week.
A number of conditions factor into the duration of a sandbox copy or refresh, including the number of customizations, data size, numbers of objects and configuration choices (for full copies), and server load. Also, sandbox refreshes are queued, so your requested copy may not start immediately after your request.
So, to answer your question, it may take a week or even more for the Sandbox refresh to complete. There's also another article, that I cannot find currently, that mentions that there are two types of refreshes, namely "slow" refreshes and "fast" refreshes. Simply put, if you have a larger data volume, you may be placed into the slower queue, while if you're doing a configuration-only refresh, you might end up in the "fast" queue. The specifics for what qualifies for each queue is not publicly mentioned, and is probably tweaked periodically to provide maximum performance.
Best Answer
As per Salesforce docs
So answer is yes you can move data in full copy and partial copy SB same concept we use in sandbox creation.
Reference