Total password count, given length and pool size First, if my password is exactly 8 characters long, derived from a pool of 95 characters, then is the total amount of passwords I can create simply $95^8$                                                                                                                                                                                  (6,​634,​204,​312,​890,​625)?

Secondly, if my password can be upto 8 characters long, derived from a pool of 95 characters, then is the total amount of passwords I can create computed the same way, or would it be something like $95^0$ + $95^1$ + $95^2$ + $95^3$ + $95^4$ + $95^5$ + $95^6$ + $95^7$ + $95^8$ (6,704,780,954,517,120)?

Is the correct term for these called permutations, or search space or key space, or...?

Thanks for the assist!
Possible combinations (permutations) = sequenceOptions to the power of sequenceLength

Assuming a pool of 95 sequence options


sequenceLength 0 = 0 permutations (950)
sequenceLength 1 = 95 permutations (951)
sequenceLength 2 = 9025 permutations (952)
sequenceLength 3 = 857375 permutations (953)
etc


This is not limited to passwords/characters. For example, when a password is put through a key derivation algorithm, it ends up as a string of bits for which there are two options; 0 and 1.  Hence, a 256 bit length key contains 2256 permutations. 

More simply, a 4-digit numeric pincode has 10000 (104) possible permutations.

As for the second part of your question, yes; if the sequenceLength were &lt;= 8 then the total number of permutations would be 950 + 951 + 952 + 953 + 954 + 955 + 956 + 957 + 958

Of course, the above assumes that each option in the sequence can appear more than once. If that's not the case then factorials come into play.