How can there be a likelihood of confusion between a trash removal service and an equipment rental service?
The trademarks are the same although one has a design. One is for the removal of trash the other is rental equipment. For example, renting a U-Haul versus a moving company. For one service, you rent U-haul to move your things, the other- the company moves your things? If the name is the same but they do different things, how is there a likelihood of confusion?
Assuming that you are trying to register a trademark, it seems that the Examiner has denied your application for a likelihood of confusion with another mark, that has the same name, but, the services are different. If a single company might perform both of those services, this is some evidence that the public might become confused. That is, the public might believe that the previously registered company is expanding its service into this new, related market. (Rather than it being a new competitor.)
On the other hand, you didn't mention which mark has the logo associated with it. And, you seem surprised, as if, a single company might not offer both of these services. This may be true. It is not likely that the Trademark Examiner is not an expert in your industry. Most likely, the Trademark Examiner provided a large number of trademarks that list both equipment rental and trash remove. Thus, the Trademark Examiner is providing some evidence that a single trademark is used for both services.
Depending on your actual situation, you may be able to present evidence or otherwise convince the Trademark Examiner to withdraw the initial refusal. I recommend consulting with an attorney for assistance. Good luck with the registration.
Also, I recommend that you read through this article on trademark office actions, if you have not already.