Memory is a solid state (no moving parts) storage medium. It can take many forms, such as RAM (Random Access Memory), flash RAM, ROM (Read-Only Memory) or EPROM (Erasable Programmable ROM). Access time for RAM is measured in nanoseconds (a billionth of a second). When memory is discussed, it usually refers to RAM (Random Access Memory) which is the computer's primary working memory. RAM is a form of storage, although it is usually temporary storage, and many people may not think of it as a storage medium, since it is volatile and loses its information when power is removed, but temporary storage is still storage.
RAM is always temporary, and requires power to retain information. When you put your computer into a hibernation state, the contents of RAM are written to file, and then retrieved when you power up your computer.
In addition to working memory, RAM is used in many areas of your computer. In most cases it is used for caching data or dedicated to specific subsystems. Most video cards will have dedicated RAM on the video card, while processors and hard drives have special high-speed RAM for caching.
The term system board describes any number of circuit boards that make up the internals of your computer, but it is used most often to describe the motherboard. The motherboard is the main board in your computer that contains the BIOS chips, RAM, I/O (Input/Output) ports, and CPU. This board maintains the electrical pathways that enable all other components to communicate with each other.
Some service manuals use the term daughter board to describe a secondary board which contains motherboard functions such as disk or I/O control. A daughter board is a board that contains some of the chips that could have been put on the motherboard but were not - perhaps due to space limitations or for other reasons. It is common to see them used in laptops and other mobile devices.