Rigidity -vs-Firmness

Rigidity : being stiff

Firmness : being determined

Being rigid is considered to be inflexible. Being firm is staying put with the purpose. To stay put with the purpose one needs to be flexible & adaptive too, which would be missing when you become Rigid.

simpler comparison Broom stick -vs- Binding wire. Wire is firm as it can flex, it still can hold things in place, however the stick, can only clean in a cluster & is held in place by a binding wire