This link will take you to look at King Aflred in more detail. http://allthingsplants.com/plants/view/120401/Trumpet-Narcissus-Narcissus-King-Alfred/
You can also look up Carlton or any narcissus /daffodil.
King Alfred is classed as Division 1, long trumpet daffodil. The cup is as long or longer than the petals. There is one bloom per stem.
Carlton is in Division 2, large trumpet daffodils. The cup length measures more than 1/3 of, but less than or equal to, the length of the petals.  There is one bloom per stem.
From the above link you can link in to Daffseek and the RHS daffodil register. I have spent the winter researching my daffodils and narcissus. It is a fascinating study. The American Daffodil Society website is also a good source of information.

The trumpets......Off for a look again.1:2
Alfred are higher too

They are both very similar in appearance. Quite frankly the difference is hardly worth bothering about.

I've seen long trumpets , wide trumpets etc. Also if grown from seed there really is no guarantee as seeds might not be true.....

There are 13 different daffodil/narcissus Divisions so that gives gardeners plenty of scope to have a wide range of interest in the garden at this time of year. They range from 3" high to over 2' so no excuse to ignore the potential joy to be had from growing them. It is a good idea to look at the differences before making a choice. I find Carlton are less likely to be flattened by the wind than the King Edwards on our exposed site.