Christmas sale?

Is there some kind of christmas sale or new years sale in Japan? When typically?

There are Fukubukuro: https://en.m.wikipedia.org/wiki/Fukubukuro

I think it�fs like in the first days of the new year. But I am not sure about the timing. Maybe it starts in the very last days of the old year. Never bought one.

Yes, Christmas (or pre-Christmas) sale goes on from early Dec. toward late Dec. And the New Year "fukubukuro" (lucky bag) sales starts typically on the 1st or 2nd of January (depending on the retailers - some open from the 1st, others on the 2nd or 3rd). But those are bags with assorted merchandise from the seller; you might not like all the items in them (you usually cannot see what's in them).

Sales discount % are not as steep as in other markets that I know of, such as the US (where 40%, 50% discounts are common).

New Year's sales are by no means limited to fukubukuro. It is one of the biggest sale periods of the year for department stores and malls, and you will find pretty good discounts on a lot of merchandise set out on tables and racks, nothing hidden and nothing left to chance. Just expect to see crowds, especially at the larger malls. I've been to Aeon Laketown (a mega-mega-mega mall in Saitama) during this time period and it was a total zoo, but there were some fairly good prices on a wide range of merchandise. I had a good time, but I got there early and left before the crowds got too big. Many corporate-run stores are open on January 1 these days; otherwise their sales will start on Jan. 2 or 3. All of the big department stores will be running big sales. There will be splashy ads on their web sites but usually they don't bother to put up much, if any, information in English.