Email migration is a process in which a large number of email messages are transferred from one email account to another email account. In general, email migration is required when you are switching email accounts. The cloudHQ email migration will transfer also all meta-data associated with emails: labels, read/unread status, sender, etc. Our migration uses Gmail API and has an average speed of ~10000 emails per day.
Email forwarding refers to the operation of re-sending email messages from your inbox to a different email address. Email forwarding is used when you want to send emails to your CRM, colleague, etc. Email forward will not preserve email meta-data (like labels and similar). Emails forwarding is using Gmail send capability so it is throttled by Google to 500 emails/day for free Gmail accounts and 2000 emails/day for paid G Suite account.