Since the digging hoe has been used all around the world for so long it has a variety of names. It is called an azada in Spain and South America, a powrah, mammoty or mamooty in India, a jembe in Africa, an enxada in Portuguese and a changkol or changkul in Asia.
The eye hoe is very common in the southern hemisphere and across Asia where the first mass produced tools were distributed by Chillington - a name the tools are still commonly called by.
The grub hoe or eye hoe was commonly used in the USA before the onset of mechanized agriculture. It is called an "Eye Hoe" because of the tapered eye socket used to attach the handle. The eye hoe is also called a Grub Hoe or Grubbing Hoe, Planters Hoe, Heavy Duty Hoe, Garden Mattock, Grape Hoe, Field Hoe, Cotton Eye Hoe, or simply a Farmers Hoe here in North America.
The grub hoe has recently become popular again in British gardening circles (where they are also calling it an Azada) thanks to the efforts of Simon Drummond at Get Digging
A digging eye hoe used for trenching is often called a Trenching Hoe, but is the same grub hoe or azada sold by Easy Digging. More info on using these tools for trenching in our Guide to Trenching and Trenchers and our new Garden Drainage Guide