What's the difference between H1-B transfer and application for a company?

If a company doesn't sponsor H1-B application, is it possible that it sponsors H1-B transfer?

For transfer, do they need to pay for it?

Thanks

Thanks for your answer.

So

1. quote means that 56k+20K,right?

2. When I start the new job, do I need to get the application receipt?

Thanks