As mentioned by /u/jellyfixh, most of the processes that modify the salinity of water (e.g. evaporation, precipitation, riverine inputs, and sea-ice formation) occur at the surface. As a result, to a reasonable approximation (ignoring the effects of mixing), you can assume the salinity of a water parcel is roughly constant once it leaves the surface of the ocean. In other words, understanding the salinity structure of the deep ocean is completely dependent on the three-dimensional circulation of the ocean interior, because the salinity of a deep water parcel is set by where that water parcel came from.

A good example of this is the Atlantic Meridional Overturning Circulation, or AMOC (which is sometimes misleadingly called the thermohaline circulation). Simply put, intense cooling and salinification in the subpolar North Atlantic results in water becoming fairly cold and very salty, which then sinks to a depth of around 2km (we call this resulting water North Atlantic Deep Water (NADW)). This water then travels south, mixing a little on the way, but mostly being dragged up towards the surface (upwelling) in the Southern Ocean, around Antarctica. There, some of the water gets pushed towards the north by the winds, freshening due to precipitation, but eventually being forced down as it sinks below the warmer, lighter waters to the north, settling at intermediate depths of around 1km (called the Antarctic Intermediate Water (AAIW)). However, some of the water upwelling around Antarctica instead moves south, freshening somewhat, but cooling intensely and forming an extremely dense water mass that sinks to the bottom of the ocean (called Antarctic Bottom Water (AABW)).

Have a look at this diagram, showing a cross-section of salinity in the Atlantic (North Atlantic on the right, South Atlantic on the left). Orange represents saltier water, blues represent fresher water. That big orange blob that goes from the surface to a depth of around 2km and moving southward is the NADW. The blue (fresh) tongue of water moving northwards and settling above the NADW is the AAIW. Finally, the blue(ish) (fresh(ish)) tongue of water sinking to the bottom of the ocean at the far left is AABW.

In the Pacific, by contrast, no deep-water formation occurs (contrary to the Atlantic). As a result, the depth-structure of salinity in the Pacific is more-or-less set by the depth-structure of salinity of deep waters entering the Pacific from other ocean basins so, whilst salinity does vary in the (subsurface) Pacific in depth, the lateral variations are fairly small compared to the Atlantic.