Cold Resistance
The resistance of the fuse. This is a parasitic fact of fuses, but is also the reason why they blow. The resistance creates a power loss which is converted to heat which melts the conductors at a specified voltage.
Voltage Rating
The maximum voltage that the fuse can operate at. This is required so the when (if) the fuse blows, the voltage will not arc over the gap created. There are commonly AC and DC voltage ratings.
Current Rating
The current rating is the maximum current before the fuse will blow. See the time-current curve for more detail. Typically, a fuse can sustain the rated current effectively indefinitely.
Fast / Slow Blow
As the name suggests, fast blow fuses blow fast, and slow blow resistors blow slowly.
Time-Current Curve
As expected, fuses do not actually blow immediately once the rated current has been exceeded, as enough energy is required to melt the fuse material. These curves show the maximum current for a given time. The difference between fast and slow blow fuses are seen here.
Breaking Capacity
The maximum current that a fuse can break. In the worst conditions, we never want the circuit to have more current than this, otherwise the fuse will not be able to break the current and remove the fault.
Littlefuse has produced an amazing fuse selection guide, attached below:
YouTube Video on fuse types for lithium battery banks: https://www.youtube.com/watch?v=SjzbQlsiiuk&fbclid=IwAR3HGmR_S5hOG78HBM0VTrcgjvHwF3CweQp2dX7nBewEkaEsjCqCXwMzlyM
Summary of the video - pay attention to the interrupting current rating on the fuses!