There is one major difference between a read-only memory (ROM) and a random-access memory (RAM) chip: ROM can hold data without power and RAM cannot. Essentially, ROM is meant for permanent storage, and RAM is for temporary storage.
Alternate explanation
A ROM chip is a non-volatile storage medium, which means it does not require a constant source of power to retain the information stored on it. By contrast, a RAM chip is volatile, which means it loses any information it is holding when the power is turned off.
Other differences between a ROM and a RAM
A ROM chip is used primarily in the start up process of a computer, whereas a RAM chip is used in the normal operations of a computer once the operating system has been loaded.
Writing data to a ROM chip is a much slower process than writing it to a RAM chip.
A RAM chip can store multiple gigabytes (GB) of data, ranging from 1 GB to 256 GB per chip. A ROM chip stores several megabytes (MB) of data, typically 4 MB or 8 MB per chip.
Computer ROM
A good example of ROM is the computer BIOS, a PROM chip that stores the programming needed to begin the initial computer start up process. Using a non-volatile storage medium is the only way to begin the start up process for computers and other devices. ROM chips are also used in gaming system cartridges, like the original Nintendo, Gameboy, Sega Genesis, and others.
AMIBIOS BIOS
The oldest ROM-type storage medium can be dated back to 1932 with drum memory. ROM-type storage is still used and continues to be improved upon for better performance and storage capacity.
Computer RAM
RAM chips are also used in computers, as well as other devices, to store information and run programs. RAM is one of the fastest types of memory in your computer and can switch quickly between tasks. For example, the Internet browser you are using to read this page has been loaded into RAM and is running from it.