Kevin,
Rivets were the only method of attaching iron and steel plates at the start of steam locomotive design. It was not later until exotic atmosphere high temperature gas welding equipment was invented and matured was it used for pressure vessels. Welding produces an almost seamless structure, stronger and less likely to leak.
A "marine" boiler in ships is the more common application of water-tube boilers, where the steam travels through pipes. Most steam locomotives use a "fire-tube" boiler, carrying the hot gasses through a pressurized body of water.
Water Tube Boiler
Marine boilers are lighter, more delicate, usually miserly of water and more efficient. Great for a ship at sea in salt water with a constant duty cycle sized to the ship and screw. A locomotive boiler is more rugged (all the jostling and coupling), heavier (more weight for traction on tires), and carries more stored energy in it (steam) for more often throttle changes. You can start a train uphill, and haul while the fireman is keeping up with running the fire.
-Nick