Etymology of Tor and Ext Functors

Ext stands for extension, as the group $\operatorname{Ext}^1(X,Y)$ parameterises extensions $Z$ fitting into a short exact sequence:

$$0\to Y\to Z\to X\to 0$$

modulo the trivial extension $X\oplus Y$.

According to Wikipedia, Tor is short for torsion, as if $r\in R$ is not a zero divisor and $B$ is an $R$-module, then $\operatorname{Tor}_1(R/(r),B)$ can be identified with the $r$-torsion part of $B$, i.e. $b\in B$ such that $rb=0$.

Torsion and Extension.............