Difference between the infinite rewriting behavior of evaluation and ReplaceRepeated

In the documentation tutorial/Evaluation it’s said that:

Every time the expression changes, the Wolfram Language effectively starts the evaluation sequence over again.

And in tutorial/EvaluationOfExpressions:

The general principle that the Wolfram Language follows in evaluating expressions is to go on applying transformation rules until the expressions no longer change.

A similar statement appears for ReplaceRepeated, too:

expr//.rules repeatedly performs replacements until expr no longer changes.

But there’re differences:

1. For ReplaceRepeated, it’s replaced just once:

   ReplaceRepeated[h[], h@x___ -> (Print@1;h@x)]
   (* h[] *)
   

2. For rewriting involving a Blank pattern, infinite evaluation occurs:

   g[x_]:=g[x]
   Block[{$IterationLimit = 20},
       g[y]
   ]
   (* Message[$IterationLimit::itlim, 20] *)
   (* Hold[g[y]] *)
   

3. For transformation rules without generic patterns such as Blank and Repeated, it’s rewrited only once.

   f[x]:=f[x]
   Trace@f[x]
   (* {f[x], f[x]} *)
   

What is the exact description of the condition for the termination of infinite rewriting?