Meaning of terms of shoe laces

What does "lace-up", "open-throat or wide-set" and "closed-throat or close-set" mean in How to Select Shoes to Wear With a Man's Suit:

Wear lace-up shoes for your most formal occasions. Open-throat or wide-set laces are less dressy than shoes with closed-throat or close-set laces.

In my guess:

• "lace-up" is some style of shoes but I am not sure what it is like and what other styles it is opposed to.
• "open-throat or wide-set" and "closed-throat or close-set" are used to specify other aspects of laces. I am also not sure what they mean.

It will be nice if there are links to details and pictures.

Solution 1:

Lace-up Shoes

Shoes that you tie up with laces. Can be either open-throat or closed-throat.

Open-Throat Shoes

The leather that holds the laces opens up at the bottom of the laces at the part closest to your toes. This causes each side to appear to split apart from one another at the bottom:

Closed-Throat Shoes

The leather that holds the laces looks like part of the rest of the shoe and doesn't open up at the bottom: