Atlantech Online's business phone page puts the two purchases side by side. You can connect to its cloud PBX, or, if you have your own PBX, it can deliver service by SIP, PRI or analog. The cloud PBX is VoIP, and so is the own-PBX route when the delivery is SIP. They differ in where the phone system lives.
On the first route, Atlantech runs the phone system. Its UCaaS page says the hosted phone system is in Atlantech's cloud in place of a PBX in your office. The phone page lists auto attendants, call distribution groups, a receptionist console and voicemail transcription, and says an administrator can add users, devices, phone numbers and call queues. It also describes unlimited nationwide calling, so public calling is part of the package. A buyer who asks for "VoIP" and means "a phone system I don't have to run" is describing this route.
On the second route, you run the PBX and Atlantech connects it. Its April 2023 post on SIP trunks says SIP trunks are for customers that already have their own VoIP PBX. The dial plan, the voicemail and the call routing stay in a system you control, and you take on its upkeep. That is the trade in SIP trunking versus cloud PBX.
Neither route is as tidy as its label suggests. A hosted service still leaves equipment at your site. People need phones or apps, and the office network has to carry the calls. Atlantech lists headsets, handsets it supplies and customer-owned devices that work with its voice switch. A trunk, for its part, does not require a PBX in your building. Twilio's requirements name an IP PBX, a SIP call server and a session border controller as examples of what a trunk can connect to. A system of that kind can run on a server somewhere else, provided it can reach the carrier.