These are a number of common battery types used in modern devices. You should be aware of the capabilities, limitations, and compatibility of the batteries used in your devices.
AA and AAA
The AA battery is widely used in flashlights, lanterns, photo equipment, etc. AAAs are used extensively in headlamps and flashlights They are available in a variety of types including alkaline, lithium, nickel metal hydride, NiCad, etc. AAs are readily available and inexpensive. Rechargeable versions normally output the same or lower voltage (normally 1.2V) and this makes then safe to use on most devices. These batteries can easily be recharged using a solar panel kit such as the Goal Zero Nomad series. Most headlamps use AAA batteries so you should keep spare batteries in your kit as well as a backup flashlight that uses the same batteries.
CR123 batteries are shorter and fatter than AAs, output 3-volts, and are normally used in tactical flashlights. They are readily available in the USA but can be expensive depending on where you buy them. A local drug store may sell a two-pack for about $19 but Cabela’s sells a 12-pack for under $30 ($8.50/each versus $2.50 each). There are rechargeable batteries with the same form factor (RCR123) but they normally output a higher voltage (3.7V). If your flashlight was not designed to use these higher voltage batteries then using them could damage your light. Some flashlights that use CR123 batteries can also use a 18650 rechargeable battery (NOT all, but some such as the Streamlight ProTac HL-x, ProTac USB, etc.).
An RCR123 is a rechargeable version of the CR123. RCR123s can output a higher voltage than normal CR123s so be sure that your device was designed for these batteries (Battery Junction kit). There are some that advertise a 3V output but I have not tested these yet. If you device was not designed to handle the higher voltage then using these batteries could damage or destroy your expensive flashlight.
The 18650 is a rechargeable battery that looks like a large AA battery. Some devices are built to use either 18650 or CR123 batteries (For example, the Streamlight ProTac HL USB). 18650s have a larger diameter than CR123 batteries.
C and D Cells
Many of the larger lanterns use the old-school C or D cells because they provide a lot of power. Many of the Coleman lanterns and the Streamlight Siege use D cells. Some spot lights and larger flashlights use C cells. Be advised that retailers often run out of D cells when storms are predicted. Alkaline versions of these batteries can have a shelf-life of up to 15 years so you can buy a brick of batteries from Costco and have then ready when needed.