What's the difference between comma separated joins and join on syntax in MySQL?

There is no difference at all.

First representation makes query more readable and makes it look very clear as to which join corresponds to which condition.

The queries are logically equivalent. The comma operator is equivalent to an [INNER] JOIN operator.

The comma is the older style join operator. The JOIN keyword was added later, and is favored because it also allows for OUTER join operations.

It also allows for the join predicates (conditions) to be separated from the WHERE clause into an ON clause. That improves (human) readability.

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FOLLOWUP

This answer says that the two queries in the question are equivalent. We shouldn't mix old-school comma syntax for join operation with the newer JOIN keyword syntax in the same query. If we do mix them, we need to be aware of a difference in the order of precedence.

excerpt from MySQL Reference Manual

https://dev.mysql.com/doc/refman/5.6/en/join.html

INNER JOIN and , (comma) are semantically equivalent in the absence of a join condition: both produce a Cartesian product between the specified tables (that is, each and every row in the first table is joined to each and every row in the second table).

However, the precedence of the comma operator is less than that of INNER JOIN, CROSS JOIN, LEFT JOIN, and so on. If you mix comma joins with the other join types when there is a join condition, an error of the form Unknown column 'col_name' in 'on clause' may occur. Information about dealing with this problem is given later in this section.

Beside better readability, there is one more case where explicitly joined tables are better instead of comma-separated tables.

let's see an example:

Create Table table1
(
    ID int NOT NULL Identity(1, 1) PRIMARY KEY ,
    Name varchar(50)
)

Create Table table2
(
    ID int NOT NULL Identity(1, 1) PRIMARY KEY ,
    ID_Table1 INT NOT NULL
)

Following query will give me all columns and rows from both tables

SELECT
    *
FROM table1, table2

Following query will give me columns from first table with table alias called 'table2'

SELECT
    *
FROM table1 table2

If you mistakenly forget comma in comma-separated join, second table automatically convert to table alias for first table. Not in all cases, but there is chances for something like this