The option to raise a new ticket or send a new email is available as part of the '+ New' quick access dropdown on the top right corner near the Search icon. You will also find 'New contact', and 'New Company' options as part of the dropdown for quick access.
+ New Ticket: This option can be used by the agents to create a new ticket on behalf of the requester, ideally after a phone call. The source of this ticket will be set as Phone. Also, on this page, you will be able to add a new contact. The 'Create another' option will open another new ticket page with the same properties as the previous ticket you just raised.
+ New Email: This option can be used by agents to send outbound emails to customers from Freshdesk, for any intimation. This email will also be converted into a ticket. Here, you will not have an option to add a contact like the one available in the new ticket page. The 'Send another' option will open another new email page with the same properties as the previous email you just sent.
If you would like to create a ticket on behalf of the customer then you can use the 'New Ticket' option and if you would like to send an outbound email to one of your customers then you can use the 'New Email' option.