"I want a green scarf."
Translation:אני רוצה צעיף ירוק.
In America (I'm from midwest and south) a scarf is a scarf. It can be long or square, a neckscarf or a headscarf, for decoration, for modesty, or for warmth. There are scarves for men and scarves for women.
I'm not sure if there are differences between different linguistic communities in Hebrew regarding what a מטפחת can mean. To me צעיף is long and is usually meant to go around one's neck, although it is acceptable to tie one around one's head for example. The big variety that goes on one's shoulders, or shawl, is usually a של "shal". מטפחת is square, usually of weaved rather than knitted fabric, big enough for putting on one's head or tying around one's neck but not to wrap one's shoulders.
What about the מטפחות that Orthodox Jews wear? Those are usually translated to English as scarves
On the east coast, no one would call a scarf a square, no matter the shape. The only clothing I can think called a square is a pocket square. No one I know calls it that (or wears one for that matter)