Diamond coated has bits of diamond embedded on the bit. Diamond pattern is just the shape the bit is cut to resemble the diamond pattern.
Rotozip is the only company that I know of that makes a bit that will cut ceramic and fit in a router. All the other bits made for this purpose are way too big and water cooled. Here is a link to the Rotozip bits;
https://www.rotozip.com/en_US/tool-detail/-/rotozip-show-product/tc1-tilecut-bit-1-pc
https://www.rotozip.com/en_US/tool-detail/-/rotozip-show-product/xb-gr125-1-8-grout-removal-bit-1-pc
The TC1 (and TC4) are made specifically for cutting and engraving in porcelain, granite, and ceramic. HomeDepot has the TC1 for around 7 bucks. Also check out Dremel bits, which is their parent company. You can also contact Drillman1 on eBay, he has a lot of inexpensive router bits for sale.