巻 is apparently the (Japanese) simplified variant of 卷. But wait. What is simpler about 巻? It looks almost same the same as 卷. Actually, it is the ‘simplified’ variant that has one stroke more. That must be why they call these characters in Japan 新字体 (new character forms) - most have simplified forms, but obviously not all.
In the cursive style the only difference is the use of bushu 26 (卩¹) instead of bushu 49 (已). In some fonts 卷 has the top strokes the other way around, something I have seen with other characters as well and thus far took to be a different printing style. Basically it is the same character but with for some historical reason a different bushu. Japanese and Chinese share words with this character (for example 圧巻・ 圧卷 (壓卷) but written with the different variants. Now let's look it up in the prewar Japanese dictionary 日蘭辭典 (1924-1936) to see what variant was used at that time.
Turns out to be the variant they still use in China! So why did the Japanese standardize 巻 instead of 卷 after the war? Henshall only writes that 巻 was ‘formerly’ 卷² and my 『漢字源』 simply states that in the 常用漢字 (1945 characters for ‘common use’) 「巻」 is used, but that the 旧字 (old form) 「卷」 can still be used as part of the list of characters that can be used in names (人名用漢字).³ Looking on the web, using Google, Yahoo or even Ask is problematic, because even though the character's variants have been given different code points in Unicode, these search engines treat them as the same character - as they do with a lot of characters that have traditional and ‘simplified’ variants. But I doubt that there is a way to escape that mechanism. Then I tried Baidu for Japan (that search engine seemed to give me both the variants) but found only simple lists.
Update: on the site 教育部異體字字典 (Dictionary of Chinese character variants [hosted by] the Ministry of Education [of Taiwan]) the page fra00454 gives a nice list of all variants of this character. It seems that at both 巻 and 卷 were used in antiquity.
1. Classified under bushu 26 卩 but strictly a variant shape (㔾 in recent Unicode. However, a lot of fonts use that code point for something that looks like a Korean glyph).
2. A guide to remembering Japanese characters, Kenneth G. Henshall. Tuttle: Tokyo, 1990.
3. 改訂新版漢字源. 学習研究社(学研): nd. (Canon wordtank V80)