As Conifold pointed out in a comment quoting the Wikipedia article cited by the OP, the difference between logical truth and tautology may be described as saying a logical truth "turns out to be true under any possible interpretation of its terms" while a tautology may be limited to "truth-function tautologies".
That Wikipedia article states the following:
Logical truths (including tautologies) are truths which are considered to be necessarily true.
Understanding that statement requires understanding three concepts: necessary truth, tautology and logical truth. The authors of forall x: Calgary Remix keep these three concepts separate which may help to clarify them.
On page 13, the authors illustrate necessary truth with this English language sentence:
Either it is raining here, or it is not.
You do not need to look outside to
know that it is true. Regardless of what the weather is like, it is
either raining or it is not. That is a NECESSARY TRUTH.
Tautologies are defined for truth-function logic (TFL) or propositional logic. They write (page 70)
...we explained necessary truth and necessary falsity. Both notions have surrogates in TFL. We will start with a surrogate for
A is a TAUTOLOGY if it is true on every valuation.
We can determine whether a sentence is a tautology just by
using truth tables. If the sentence is true on every line of a complete truth table, then it is true on every valuation, so it is a
One can think of a tautology as a truth dependent only on logical connectives such as "and", "or" and "not" between sentences.
A logical truth is a similar situation but in first order logic (FOL) rather than truth-functional logic where one has in addition to the logical connectives of truth-functional logic quantifiers and equality. Rather than valuations found in a truth table one now refers to interpretations: (page 225)
An FOL sentence A is a LOGICAL TRUTH if A is true in
In summary: The concept "necessary truth" refers to a natural language sentence such as found in English which is always true. A "tautology" refers to a sentence of truth-functional logic where every valuation, every row of a complete truth table, evaluates to true. A "logical truth" is a sentence in first order logic where every interpretation is true.
P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/
Wikipedia, "Logical truth" https://en.wikipedia.org/wiki/Logical_truth