A resonance (in the particle physics or related physics sense) and an unstable particle is exactly the same thing. The object has some complex mass and the imaginary part determines the decay width (and decay rate). But these two terms describe different aspects of the same thing.
"A particle" refers to the object, the particle species (in your URL's case, it's composite particles i.e. bound states, often excited states), and all conceivable properties it may have and processes it may undergo.
On the other hand, a "resonance" only describes one particular aspect of the object (particle), and the corresponding method how it may be discovered, namely its ability to produce a local peak ("bump") in a graph of a cross section as a function of energy. It's usually a cross section of a process with the particle in the initial state and a two-particle or multi-particle state in the final state, or vice versa.
The cross section goes up when the "energy is right" to produce (or come from) a particle of the particular mass. The local peak has the same mathematical reason as the resonances anywhere in physics – e.g. when a radio is amplifying the signal at a given frequency. When the frequency (or energy, and $E=hf$) is right, plus minus the width, the strength (or, in quantum mechanics, the probability) of a process is much higher.
When we see such a "bump", we may discover a new particle. That's how the Higgs boson was discovered in 2012 – and many other particles before the Higgs, too. The actual unstable particle, e.g. the Higgs boson, may also enter many other processes that can't be described as a simple resonance. It may be produced together with the Z-boson and/or other particles, for example, and in these more complicated processes, the Higgs boson is no longer a "resonance".