permeakra is quite right with his counterexamples of salts that don't taste purely salty, but I'd like to expand on why. We haven't fully identified and elucidated the receptors involved in taste, but they can be broadly classed into tastes people are familiar with: salty, sweet, sour, bitter, and umami.
Salty and sour receptors are both known to be mostly dominated by ion channels, where salty receptors allow small cations to pass and sour receptors are sensitive to pH in a similar fashion. The other receptors are g-protein coupled receptors. The trick with taste (and smell, for that matter) is that there is not a single receptor type for each possible chemical one can taste, i.e. there's not a receptor entirely selective towards $\ce{Na+}$. The way it works is that there are many types of taste receptors that are somewhat selective to specific classes of molecules and a given molecule may induce a response in many different receptors. The brain takes all the data from all these receptors; combines them; integrates information from the nose, eyes, ears, tactile nerves in the mouth, etc.; and then produces the sensation of taste.
Thus, though both $\ce{Na+}$ and $\ce{K+}$ will stimulate some of the same saltiness receptors, they also stimulate other receptors and in different amounts, making them taste different. In general, small cations can stimulate the ion channel receptors for saltiness, so many salts do taste salty to a certain extent, but many also stimulate other receptors. Because what we perceive as taste comes from the interaction of all these different receptors (as well as other senses), one salt may taste very salty and another quite bitter, despite both activating saltiness receptors; the responses are not independent (which is why it's possible to mask overly salty soup or whatever by adding sugar).