Steve,i've an identical small side-axe to your last couple photos.I used as prescribed,as a carpenter's hatchet.(Most satisfactory tool,we've been happy together many years).
As a smith,i can clearly discern some individual hammer-blows that helped shape that tool,and it has most definitely been forged "by hand".
Among the US,British,and Canadian smiths,this subject has come up regularly-what constitutes "Hand"-forged,-made,et c.
The informal consensus seems to be that to qualify as such the forging must have been Held by a living hand while forged.
Now,i've a couple of points to make:First,that the largest mass that it is Possible(as in Reasonable,and/or on a basis of constant,repeated work) to forge by hand Literally(as in holding it And administering the forging blows),is roughly 5/8" square stock.(alas and alack).
That means that ANY (solid)forging that weighs more than a pound or so has had some sort of Power applied to it's forging.
That extra "power" may've been one or more strikers,or a power-hammer of whatever sort(waterwheel-driven helve-hammers date back to 16th century and earlier,for example).
It really helps to distinctly differentiate between the Pre-,and the Industrial Age era forging.Before that age of machines (that we so take for granted),most axes,for example,were of course composited using several different pieces(up to about 7,to the best of my personal knowledge).
The image of a smith as a loner is,of course,Entirely misinformed.Rarely was it that forging was accomplished with less than 3,often-many more assorted professionals involved.
The reason for that is that is that inescapable difference between a Forging,and a Riveting blow.The first,penetrating the mass of a forging throughout,causes minimum of internal dislocations,and is an absolute MUST in any plastic deformation(the official definition of "forging")-based work.
Please excuse my hectoring tone,by no means i intend to lecture at all,let alone anyone in particular.....
It's just,again,as a smith,i often feel misunderstood,and unjustly slighted,when i hear/read mention of "such and such is a Machine-made axe,so why in @##ell is it so expensive?!",and other opinions overtly or less so implying that smiths,for avaricious,alterior motives,are skimping on all that "hand-work"!

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And i know that in speaking to many of you i'm preaching to a choir,but i'll go ahead and say this anyway:The visible(and often irregular)tool-marks are a sign of a smith loosing control.NEVER a good thing,structurally,metallurgically and all other important senses.
In the past,properly forged object did not appear all banged up,but quite the opposite.Only in the last several decades is the "forged look" comes creeping in,as a reaction to all the machine-finishes surrounding us everywhere....
Or,like in that hatchet above,they're a result of expediency,and are left around all the non-critical to function of the tool places.