sudar and sweater

In Modern Hebrew we find two words with the same consonants, but different vowels:
סוּדָר - sudar - "scarf, shawl"
סְוֶדֶר - sveder - "sweater (or jumper)"

Is there any connection between them?

The word sudar is from Talmudic Hebrew, and many of us are familiar with it from the term kinyan sudar קנין סודר - a contractual agreement where one of the parties lifts up a sudar - a handkerchief owned by the other. This is still done at Jewish weddings today.

Klein points out that the word is actually a

back formation from supposed plural סודרין, a word borrowed from Greek soudariom, from Latin sudarium (= handkerchief), literally: "cloth for wiping off perspiration' from sudor ( = sweat, perspiration). Latin sudor derives from IE base sweid-, swoid-, swid- ( = to sweat).

As proof to this, Almagor-Ramon writes that we find sources that have sudarin סודרין as a single noun. For example, in this edition of Mishna Sanhedrin 7:2, we find the term "סודרין קשה" - "a coarse sudarin".

The English word "sweat" derives from the same Indo-European root Klein mentioned above, and not surprisingly, the word "sweater" comes from "sweat". However, unlike the sudarium, which was meant to remove sweat, "sweater" has the opposite meaning. From the Online Etymology Dictionary:

"woolen vest or jersey, originally worn in rowing," 1882, from earlier sweaters "clothing worn to produce sweating and reduce weight" (1828)

So a sudar gets rid of sweat, and a sweater encourages sweat.

While there have been attempts to have Modern Hebrew adopt sudar for "sweater", they haven't succeeded well, probably due to the familiarity of the term sudar as scarf. Purists must grimace, but not only do Israelis say sveder for "sweater", but they even use סווצ'ר svecher - for "sweatshirt".