Describing their difference at a somewhat rudimentary level: contemporary makes reference to the present-day – that which is current and of the time – whereas modern alludes to the past specifically that of Modernism (post the First World War) and mid-20th century modern design and architecture.
Admittedly this is not a style for everyone and you need both an appreciation for the ‘old and used’ furniture along with ample patience to get the right look.
For a coastal beach theme you can really have fun with the decor. Go all out with sea-inspired wall art pieces of coral and shades of blue and other soft/neutral colors. Pottery Barn even has these lovely sheets to go along with your beach look.
There are all sorts of different DIY headboard projects you can take on to create something that’s really unique for your bedroom but perhaps the easiest way to do it is by simply using a regular bookshelf.