Are nondeterministic algorithm and randomized algorithms algorithms on a deterministic Turing machine? An algorithm on an abstract machine is a finite sequence of operations of the machine. (Correct me if I am not correct.)

However, there are
different kind of algorithms, such as deterministic, non-deterministic,
and randomized algorithms, and possibly others.

Are these algorithms running on deterministic Turing Machines, or do
they have to be run on specific machines? For example:


Are nondeterministic algorithm algorithms on a deterministic Turing
machine? I heard that they are not, but are on nondeterminisitic
Turing machines, but I forget where I heard it. Or I might be wrong.
Are randomized algorithms algorithms on a deterministic Turing
machine?
Broadly speaking, you can normally trade the word "algorithm" for the words "Turing Machine", in the sense that a Turing Machine is not a programmable computer like the one you have in front of you, it is a mathematical embodiment of an algorithm. So for the two cases you mention:


A nondeterministic algorithm is a nondeterministic Turing Machine.
A randomized algorithm is a probabilistic Turing Machine.