Flash memory storage and EEPROM both use floating gate transistors for storage of data. What differs between the two and why is Flash so much faster?
The first ROM devices had to have information placed in them via some mechanical, photolithographic, or other means (before integrated circuits, it was common to use a grid where diodes could be selectively installed or omitted). The first major improvement was a "fuse-PROM"--a chip containing a grid of fused diodes, and row-drive transistors that were sufficiently strong that selecting a row and forcing the state of the output one could blow the fuses on any diodes one didn't want. Although such chips were electrically writable, most of the devices in which they would be used did not have the powerful drive circuitry necessary to write to them. Instead, they would be written using a device called a "programmer", and then installed in the equipment that needed to be able to read them.
The next improvement was an implanted-charge memory device, which allowed charges to be electrically implanted but not removed. If such devices were packaged in UV-transparent packages (EPROM), they could be erased with about 5-30 minutes' exposure to ultraviolet light. This made it possible to reuse devices whose contents were found not to be of value (e.g. buggy or unfinished versions of software). Putting the same chips in an opaque package allowed them to be sold more inexpensively for end-user applications where it was unlikely anyone would want to erase and reuse them (OTPROM). A succeeding improvement made it possible to erase the devices electrically without the UV light (early EEPROM).
Early EEPROM devices could only be erased en masse, and programming required conditions very different from those associated with normal operation; consequently, as with PROM/EPROM devices, they were generally used in circuitry which could read but not write them. Later improvements to EEPROM made it possible to erase smaller regions, if not individual bytes, and also allowed them to be written by the same circuitry that used them. Nonetheless, the name did not change.
When a technology called "Flash ROM" came on the scene, it was pretty normal for EEPROM devices to allow individual bytes to be erased and rewritten within an application circuit. Flash ROM was in some sense a step back functionally since erasure could only take place in large chunks. Nonetheless, restricting erasure to large chunks made it possible to store information much more compactly than had been possible with EEPROM. Further, many flash devices have faster write cycles but slower erase cycles than would be typical of EEPROM devices (many EEPROM devices would take 1-10ms to write a byte, and 5-50ms to erase; flash devices would generally require less than 100us to write, but some required hundreds of milliseconds to erase).
I don't know that there's a clear dividing line between flash and EEPROM, since some devices that called themselves "flash" could be erased on a per-byte basis. Nonetheless, today's trend seems to be to use the term "EEPROM" for devices with per-byte erase capabilities and "flash" for devices which only support large-block erasure.
Spoiler: EEPROM is in fact Flash.
As supercat's answer brilliantly pointed out, EEPROM is an evolution of the older UV-eraseable EPROMs (EEPROM's "EE" stands for "Electrically Eraseable"). However, despite it being an improvement to its old pal, today's EEPROM's way of holding information is the exact same of the flash memory.
The ONLY major difference between the two is the read/write/erase logic.
NAND Flash (regular flash):
Can only be erased in pages aka. blocks of bytes. You can read and write (over unwritten) single bytes, but erasing requires wiping out a lot of other bytes.
In micro-controllers, it's generally used for firmware storage. Some implementations support flash handling from within the firmware, in which case you can use that flash to hold information as long as you don't mess with used pages (otherwise you'll erase your firmware).
NOR Flash (aka EEPROM):
Can read, write and erase single bytes. Its control logic is laid out in such way that all bytes are accessible individually. Although it's slower than regular flash, this feature benefits smaller/older electronic devices. For instance, older CRT TVs and monitors used EEPROMs to hold user configurations such as bright, contrast, etc.
In micro-controllers, that's what you generally use for holding configurations, states or calibration data. It's better than flash for that as for erasing a single byte you don't have to remember (RAM) the contents of the page to rewrite it.
There's a common misconception that NOR Flash uses NOR gates while NAND Flash uses NAND gates (and in fact it seems obvious). However that is not true. The reason for the naming is the resemblance of the control logic of each memory type with the NAND and NOR gate schematic symbols.
Flash is a type of EEPROM (Electrically Erasable Programmable Read-Only Memory). "Flash" is more of a marketing term than a specific technology. However, this terms has sortof converged to mean a type of EEPROM that is optimized for large size and density, usually at the expense of large erase and write blocks and lower endurance.
Flash memory is a variation of EE-PROM that is becoming popular.The major difference between the flash memory and EE-PROM is in the erasure procedure.EE-PROM can be erased at a register level,but the flash memory must be erased either in its entirety or at the sector level.
"Flash" storage is a catch-all term for storage inside memory chips(Non-Volatile Memory), rather than spinning disks like Floppy disk, CD, DVD, Hard disk, etc.
NOR and NAND are the original flash memory chips, and was invented by Fujio Masuoka while working for Toshiba circa year 1980. "NOR" and "NAND" are used in most USB thumb drives.
Flash storage also includes both EEP-ROM (electrically erasable programmable read-only memory) and NV-RAM (Non-Volatile Random-Access Memory). EEP-ROM is cheaper, and used for storage in most System-on-Chips and Android devices. NV-RAM is more expensive, and used for Solid-State Drives and storage in Apple devices.
The new NV-RAM chips are much faster than EEP-ROM and other Flash technologies.
For more Info, see: http://www.crifan.com/___flash_memory_nand_eeprom_nvram_and_others_zt/