Refers to a decorative or graphic design, such as on fabric, ceramics, cards, or packaging. Often implies a repeated or distinctive visual motif.
This cup has a floral design on it.
The pattern on this kimono is very gorgeous, isn't it?
I liked the design on the back of the playing cards.
Choosing the design for a stamp is fun.
The new banknote has a different design.
デザイン is a general loanword covering design in any field (graphic, industrial, etc.), whereas 図柄 is narrower, referring to the visual pattern printed or drawn on an object.
柄 is a casual, everyday word for pattern (as on clothing), while 図柄 sounds a bit more formal and is often used for printed or artistic motifs.
意匠 is a formal, often legal/design-industry term for a design (as in patent law), while 図柄 is the everyday word for the visual pattern itself.
絵柄 refers specifically to a pictorial or illustrative design (like a printed picture), while 図柄 covers designs more broadly, including abstract or geometric patterns.
Compound of 図 (zu, 'drawing, figure') and 柄 (gara, 'pattern, design'). The reading ずがら is a standard combination of the on'yomi of 図 and the kun'yomi of 柄.