I strongly doubt that there would be confusion -- especially if the products were in different lines of business. But file for your own trademark and get real protection.
With the examples given, it seems unlikely that there would be a conflict between the two names. However, the “Silver Bug” and “Silvered Wares” names were Hereandthere’s examples only.
If you replace the “silver” that is used in both names with a famous name, you can see how that can change the assessment.
The names are trademarks in the same class of goods/services, too, so similarity can become more of an issue.
“Silver” also would be a unique identifier for a brand of beer and could therefore have greater trademark protection than another word might have. It is an “arbitrary” mark and arbitrary marks are considered strong marks.
The real name Hereandthere is considering, in other words, could indeed infringe on the rights of the other trademark holder. The specific names matter. That is why it would be smart for Hereandthere to have a trademark law professional personally review the real names involved.
Trademark rights, by the way, are gained by the use of the trademark in commerce. In the US, it will be the first user of a mark who is the presumed owner of the mark. Trademark registration is not required.