Learn English – Which of the following word is matched to the sentence

First, matched doesn't make sense in your examples: This would be used if the items were already paired/sorted:

After the selecting process, the matched items are displayed.

The other two depend on context:

A. If it matches any of the items, the item is selected.

Take an item X. Compare it to a set of items. If in the set is another item X', choose X, else discard X.

B. If it matches any of the items, the matching item is selected.

Take an item X. Compare it to a set of items. If in the set is another item X', pick X', else ignore X'.

Real world example: You go shopping with your child.
A. Your child brings you a can of pineapples. If canned pineapple is on your shopping list, put it in the cart, else put the can back on the shelf.
B. Your shopping list has canned pineapple on it. You go to the shelf with canned fruit. If there is a can of pineapple, put it in your cart, ignoring the canned peaches.

"Stuff" is informal, especially when used as a de facto pronoun. "Stuffs" is normally used as a verb, not as a plural pronoun.

"Thing" is a standard pronoun, so it can be used in both formal and informal writing. "Things" is a normal plural pronoun.

I am going to give my children food, clothes, and other things.

sounds formal. "I am going to", "give", and "children" are all formal choices of words.

I am going to give my children food, clothes, and other stuff.

sounds informal enough to almost seem incorrect. Using "kids" instead of "children" would make the sentence more consistently informal. Using colorful metaphors (like "put clothes on my kids' backs" or "put food in my kids' bellies") would also be more consistently informal than "give my children <things>".

In informal speech, it is normal to use contractions for some words. Even in informal writing, it is normal to transcribe these words using the full words. Thus, your written "I am going to give" might be spoken informally as "I'm gonna give".