I can see other stores products in my store search

It might be that you are looking up your store in the search function under the Suggestions area rather than the Collection.

If you store name has other related searches including products and other stores the suggestions area shows this as a search option.

In this example I've used the phrase ' the bag lady' and you can see under suggestions the bag lady shows as an option. Selecting this will show all related products and stores to this phrase.

As there is a store also called The Bag Lady this will show in the Collections area at the bottom and is a direct link to the makers store.