So this is a question of English more so than anything.
There are contexts where any 2 or sometimes even more of these words all mean the same thing, and there are contexts where they are different. What I’ll do is for each word state it’s most common context (and Full disclosure this come with all my biases) and what it’s mean there:
Function: A set of pairs constructed from two sets called the domain and codomain. Where the function can be seen as a abstract (meaning “imagined” here) machine that consumes values from the domain and produces values from the codomain.
Operator: usually in higher math and physics contexts is a function whose domain includes other functions. Computer Scientists call these “higher order functions”
Algorithm: A function with a well defined abstract I mplementation. Rather than just being a set theoretic invention (i.e a set of pairs as functions are generally defined), algorithms are functions whose internal operation/ calculation has a story. In the earlier analogy from functions, the abstract machines of algorithms can actually picked apart and described. Its possible to talk about how long the machine runs, what subcomponents it has, how much space it uses etc...
Procedure: a super set of Algorithm, procedures don’t have a connotation of mapping inputs to outputs, although they can if you want.
Operation: a substitute for the word function usually used when you want to treat the function as a single atomic object. Ex: order of operations (here functions are the little things, and we are looking at a larger idea of how to evaluate them, what order, etc...). Another example: Quicksort takes O(n log n) floating point operations on randomized inputs. Here operation is short hand for: addition, subtraction, division, multiplication, comparison. But those functions and their inputs (integers) really aren’t the main point. The main point is we want to count how many times we do them, so we call them operations to make this context clear.
Now remember, if you put any amount of effort you will find situations where these distinctions are blurred and these words replace each other.
This is just a casual heuristic that I think will serve as a good rule of thimb.
Best Answer
"Meta" means something like "mentally take a step back and look at what your doing". Compare https://en.wikipedia.org/wiki/Metaphilosophy.
In my experience this is actually what you do when calculating a "hyperoperator". That's why I'd actually argue, "metaoperator" would be a more appropriate name for it.