Hand-stamping and engraving are both options on many of my products. It does help to know what hand-stamping is before you purchase an item with this option.
Hand Stamping involves using a hammer and individual metal letter stamps, and hammering the name onto the item. A fair amount of pressure is used, and quite often the indentation can be seen on the reverse of the item. It can also be off centre a little, but this should be seen as a unique quality of the item rather than a fault. The benefit of hand-stamping means you are giving a gift with a ‘hand-made‘; look, and letters can also be blackened to make the text stand out (or ‘pop‘).
Engraving, on the other hand, is a very exact way of personalising an item. I have a machine (which, by how much it cost me, should have a steering wheel attached so I can drive it around!) that can place the text exactly where I want it, it leaves no indentations, and there is a fair amount of freedom to change things and fit things in. BUT, the letters cannot be blackened.
It is all up to personal choice, but having the knowledge to know the difference means you have a better understanding of how your item will look when you receive it.