Plutonium and Uranium are actinides Rare earths for the purpose of discussion on mining are many of the lanthanides (some have little, if any known economic use), scandium & yttrium.
These two groups have totally different properties. The term of 'rare earths', sometiems to encompass both is purely historic (ie due to difficulty in isolation)
To state, in the context of the thread, that rare earths include actinides shows a total misunderstanding of chemistry.