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ASSP: "standard" product, such as DRAM, VRAM(Video DRAM), SGRAM(Graphic DRAM), 8051, .... etc. It is "standard" product but still "application-specific".
So from my point of view, an ASIC can be an ASSP.
Example: 8051=>ASSP ("standard" product)
8051-Embedded USB keyboard/mouse controller => ASIC
In computers, an ASSP (application-specific standard product) is a semiconductor device integrated circuit (IC) product that is dedicated to a specific application market and sold to more than one user (and thus, "standard"). The ASSP is marketed to multiple customers just as a general-purpose product is, but to a smaller number of customers since it is for a specific application. Like an ASIC (application-specific integrated circuit), the ASSP is for a special application, but it is sold to any number of companies. (An ASIC is designed and built to order for a specific company.)
An ASSP generally offers the same performance characteristics and has the same die size as an ASIC. According to a Dataquest study, 17% of all semiconductor products sold in 1999 were ASSPs; 83% were general-purpose. According to Dataquest's Jim Walker, the trend is toward more application-specific products.