"Automatically" vs "In an automated manner"

Is there any difference between automatically and in an automated manner? For example,

Automatically

He's been made redundant, as all of his tasks are now done automatically.

Automated

He's been made redundant, as all of his tasks have been automated.

They are similar but sometimes distinct, as might be seen from comparing

He was brought up to say thank you automatically

with

He was brought up to say thank you in an automated manner

The former is about consistent courtesy. The latter is about talking like an automaton.

In the examples in your question, I might take the first example to mean the machines he used to operate do not need him any more, while the second might mean that new machines had replaced him. It depends on the context.

I think that 'in an automated manner' is most usually used to describe a mechanical process, whereas 'automatically' is equally used for human actions and mechanical processes.

I believe the use of these adjectives depends on wether you are talking about the process/method/implementation with which something is done, or talking about the actual execution or result of that process.

Automated refers to the process:

The factory is automated

Automatic refers to the execution of the process:

The car production is automatic

While it is harder to apply that distinction for more abstract concepts, it is in general possible to distinguish between a process and its execution.

The difference between "automatically" and "in an automated manner" should then be clear. The "manner" or the "tasks" correspond to the process, and thus are "automated". The "done tasks" are the result of the process, and their execution is "automatic", they are "done automatically".