How to translate "knitting" and "weaving" into Mandarin?
According to the ABC Chinese-English Dictionary, the Chinese word 编织 can mean "weave; knit; plait; braid".  ABC is saying it's a general word that can mean all of these things.  If you want to distinguish between these things then you might need a different word instead.

If you look up "weaving" on Wikipedia and press Languages / Chinese, it takes you to a Chinese article called 梭织.  ("Knitting" takes you to 编织.)  Although in general it is wise to be a bit careful when using Wikipedia (check the sources etc), I would be very surprised if an article title (especially for a long-established article like "weaving") would not have been corrected if it were wrong.  梭织 is not in the ABC but 梭=shuttle in textiles (compare 梭子) and 织 can mean to weave or to knit (compare 组织=organize) so it looks very plausible that 梭织 specifically means weaving with a shuttle.

ABC also says the word 针织 (from the question) means to knit but not to weave; the first character 针 means needle.

So simply put 针织 for knit, 梭织 for weave, and 编织 as a catch-all term that could mean either.