I suppose a good example of a contemporary science vessel would be Cousteau's Calypso. No doubt the Coast Guard has different kinds of ships, like the kinds of ice cutters and research vessels that visit the Arctic extremes.
Picard repeatedly mentioned science vessels (or the occasion to dispatch them) in episodes like TNG's "Relics", further underscoring a difference between Federation starships-of-the-line and dedicated science ships. To expand on this: yes, a starship like the Enterprise could be used as a science vessel, and ships like her probably do serve in that capacity from time to time. But it would be a waste to dedicate a ship like the Enterprise to that task, full-time. A dedicated science vessel would be like a survey team's or science team's expedition. Some missions may allow for the construction of a space station. Other missions may be handled with a team being deposited on a planet surface to set up camp in an alien wilderness. But some efforts, especially those requiring mobility in deep space, may require a vessel tailored to the needs of the expedition. (Surveying nebulae or dark matter may be an example.)
In the context of ENT, Archer's NX-01 was Earth's first attempt to build a working Warp 5 starship-of-the-line. But in order to do that, Earth had to launch a primitive vessel and send it into deep space to discover what a starship-of-the-line needed in order to be effective. While there were many things to criticize about ENT, the inadequacies of the NX-class were deliberately written into the stories to underscore that Earth's Starfleet was the new-kid-on-the-block, and still had to figure out what they were doing in space.
Picard repeatedly mentioned science vessels (or the occasion to dispatch them) in episodes like TNG's "Relics", further underscoring a difference between Federation starships-of-the-line and dedicated science ships. To expand on this: yes, a starship like the Enterprise could be used as a science vessel, and ships like her probably do serve in that capacity from time to time. But it would be a waste to dedicate a ship like the Enterprise to that task, full-time. A dedicated science vessel would be like a survey team's or science team's expedition. Some missions may allow for the construction of a space station. Other missions may be handled with a team being deposited on a planet surface to set up camp in an alien wilderness. But some efforts, especially those requiring mobility in deep space, may require a vessel tailored to the needs of the expedition. (Surveying nebulae or dark matter may be an example.)
In the context of ENT, Archer's NX-01 was Earth's first attempt to build a working Warp 5 starship-of-the-line. But in order to do that, Earth had to launch a primitive vessel and send it into deep space to discover what a starship-of-the-line needed in order to be effective. While there were many things to criticize about ENT, the inadequacies of the NX-class were deliberately written into the stories to underscore that Earth's Starfleet was the new-kid-on-the-block, and still had to figure out what they were doing in space.