Both ... and more!
The ocean floor rises and falls due to tectonic activity and also due to the pressure exerted by water. So, for example, we know around Alaska that the ocean floor is being compressed downwards by the additional weight produced by the increased volume of water from melting glaciers. This means the melt water won't raise sea levels relative to Alaska's coast as much as otherwise would be the case. A lot of land masses in the Northern Hemisphere are still rebounding upwards as they recover from the weight of glaciers during the last Ice Age. The actual level of the sea, relative to the coast, also depends on the shape of inlets, currents, tides, and prevailing wind direction.
How do we know that sea levels are actually rising? What scientists have done is map the topography of the planet. They also map the gravitational forces around the planet (which changes depending on the density of rock at any given location). Using this information they then build up a 3D model surface that accounts for both the difference in gravitational forces water would be subject too AND the shape of the ocean beds and coastlines themselves to provide a global reference. Our satellite systems then provide data so they can measure the position of the ocean surface relative to this 3D model surface. That 3D surface is updated every few years as more mapping data comes in.
So, relative to this 3D surface, sea levels are rising at a rate of just over 3 millimeters a year. If you take this model surface and remove the gravitational effect, then you can see how that affects sea levels relative to coasts on a local level which will not necessarily mean higher depending on shape of inlet and gradual rise of landmass.
Tidal gauges, on the other hand, measure sea level relative to a 'fixed' point on land, which could of course not be fixed at all. This is why there is a seeming discrepancy between tidal gauge and satellite measurements. When you readjust the tidal gauge results so they are relative to the same reference model as satellites, they also show a global rise in sea levels.
So ... sea levels are definitely rising. That doesn't mean rising at every inlet or along every coastline.