Short answers, pulled from the story.
An application-specific integrated circuit is a chip customized for a single, particular use rather than general-purpose computing. Examples include chips designed to run in digital voice recorders and high-efficiency video codecs. Modern ASICs can integrate entire microprocessors, RAM, ROM, flash memory, and other large functional blocks on one die, a configuration called a system-on-chip.
Robert Lipp developed the first CMOS gate arrays in 1974 for International Microcircuits, Inc. CMOS technology opened the door to broad commercial adoption of gate array design.
Sinclair Research used gate array circuitry in the ZX81, introduced in 1981, and the ZX Spectrum, introduced in 1982. The company used these chips primarily as a low-cost input/output solution for handling the computers' graphics.
An ASIC is customized for one specific use and cannot be reprogrammed once fabricated. A field-programmable gate array (FPGA) can be configured by the user for many different applications. FPGAs tend to be more cost-effective for smaller designs or lower production volumes, while ASICs suit very large production volumes where high non-recurring engineering costs can be spread across many units.
A soft macro is an IP core delivered as a hardware description language file, making it largely process-independent and usable across different manufacturers. A hard macro is a fully routed design that can be printed directly onto an ASIC mask, but it is limited to a specific manufacturing process and usually requires additional work to migrate to a different process or manufacturer.
An application-specific standard product implements a specific function but is sold as an off-the-shelf component to a wide market, whereas an ASIC is typically designed by or for a single customer. Ethernet network interface controller chips and flash memory controller chips are examples of ASSPs.