Your theory is mostly correct.

1. the cap is a cover for a bottle

Yes

2. the lid is a cover for a container which is not bottle

Yes

3. the lid doesn't have a screw in it. If it has screw, it is called a cap.

No. Lids often have screw tops. That feature isn't relevant.

Coke cans

Soda cans usually have pop-tops, which is arguably a type of lid. It is not a cap.

Standard cans like pinto beans or mandarin oranges have a lid. The lid requires a can opener, or sometimes has a ring to pull it off. Manufacturers in the USA should strongly consider adding those rings more frequently because they are quite convenient.

Your theory is mostly correct.

1. the cap is a cover for a bottle

Yes

2. the lid is a cover for a container which is not bottle

Yes

3. the lid doesn't have a screw in it. If it has screw, it is called a cap.

No. Jars often have screw tops. That feature isn't relevant.

Coke cans

Soda cans usually have pop-tops, which is arguably a type of lid. It is not a cap.

Standard cans like pinto beans or mandarin oranges have a lid. The lid requires a can opener, or sometimes has a ring to pull it off. Manufacturers in the USA should strongly consider adding those rings more frequently because they are quite convenient.

Your theory is mostly correct.

1. the cap is a cover for a bottle

Yes

2. the lid is a cover for a container which is not bottle

Yes

3. the lid doesn't have a screw in it. If it has screw, it is called a cap.

No. Lids often have screw tops. That feature isn't relevant.

Coke cans

Soda cans usually have pop-tops, which aren't called lids or caps. Thus, you don't refer to a soda can having a lid or a cap.

Standard cans like pinto beans or mandarin oranges have a lid. The lid requires a can opener, or sometimes has a ring to pull it off. Manufacturers in the USA should strongly consider adding those rings more frequently because they are quite convenient.

Your theory is mostly correct.

1. the cap is a cover for a bottle

Yes

2. the lid is a cover for a container which is not bottle

Yes

3. the lid doesn't have a screw in it. If it has screw, it is called a cap.

No. Lids often have screw tops. That feature isn't relevant.

Coke cans

Soda cans usually have pop-tops, which is arguably a type of lid. It is not a cap.

Standard cans like pinto beans or mandarin oranges have a lid. The lid requires a can opener, or sometimes has a ring to pull it off. Manufacturers in the USA should strongly consider adding those rings more frequently because they are quite convenient.