I have read a very interesting discussion here:
https://forum.musicasacra.com/forum/discussion/14711/where-to-buy-surplice#Item_18
A highlight:
"THE garment to have ‘in choir’ is a surplice, which, worn over a cassock is ‘choir habit’.
A surplice is a full white garment that reaches to approximate ankle length, though the faint of heart wear them at least to somewhere below calf length. This is what a surplice is. Anything shorter than this is to a surplice what our tail bone is to a tail…
Things that aren’t surplices at all, but are vestigial remnants of surplices - One of these items is the so-called
cotta, which is nothing more than a chopped off surplice. Cottas generally reach anywhere from above the waist to near the nipples.
Some people seem really to like putting these piteously vestigial things on very little boys. I don’t know the history of the cotta, but its history is not a very lengthy one.
One finds these ridiculous looking rags on little boy altar servers at churches which apparently believe that they are more Catholic and more traditional. They aren’t. Anything above the calf, no matter how many people wear them, is not a real surplice. The so-called cotta (some of them are so short that they look like flouncy brassieres with funny little bitty sleeves) is something that shouldn’t exist, and historically didn’t. More amusing than one of these cottas on little boys is one on a grown man.
It is interesting that after the council all the ‘progressive’ parishes began to put their altar servers and acolytes in albs. This, oddly, is the historical vesture for acolytes and servers, preferably worn with an amice, preferably appareled. Ironically the ‘traditional’ parishes hung onto cassock and surplice as sanctuary vesture, thinking it more historic and traditional. It isn’t at all! Its tradition as sanctuary vesture is quite short. Cassock and surplice are choir habit, not sanctuary vesture. So, the joke is on the ‘traditionalists’. But, traditionalists and contemporaryists have one thing in common - nobody can tell them anything."