This is a really subjective subject. Different companies have different policy.
But general rule of thumb is executive represent management, non-executive represent not critical decision making therefore is unable to represent the firm.

(There is a legal definition to it)

But a summary, executive gets better perk/salary/benefit then a non executive. Just because you're a non executive, doesnt mean you can't move up. There are plenty of stories where people join as a clerk and work their went up to directors.

There's no hard & fast definition of executives and non-executives in the context that you're thinking of. It's a title that is overused... like analyst. They might not really execute or analyse anything. Sometimes it implies a graduate position but the line is very, very blurry.

The only formal definition of executive is to mean someone who can execute actions for the company ie. a person authorised to represent and commit the company to legal contracts. These are the board of directors and the management ie. CEO, CFO, COO/GM, Legal Counsel and Company Secretary.

the definition of executive in malaysia totally the reverse of what it mean in US. where executive are senior management, that is why the CEO the top position in the company is the chief executive officer. in malaysia executive generally are the entry level jobs above clerk level.

my old company is an american company the top person in my company title is country executive, causing problem with malaysian perception that executive are low level worker, so have to get US approval to change title to something like country director.

No. It means that the title has little meaning in terms of career progression. What matters is the size of your responsibilities and how much you're paid ie. how much you are worth to an employer. The company can call you CEO (Chief Executive Officeboy) if they want... but you're still just an officeboy.