Just like Mendel's ideas have been proven by the existence of DNA, Hebbian learning can be explained by STDP. That doesn't make Mendel's or Hebb's teachings obsolete.
STDP is the long-term synaptic potentiation or depression governed by the timing of pre- and post synaptic cell firing. STDP depends on certain “critical windows” for spike timing. This critical window is on the order of tens of milliseconds (Dan & Poo, 2004). STDP is known for quite some time, but is by far a more novel idea than the idea of Hebbian learning posed in the 1940's (Markram et al., 2012). Hebbian learning has been popularly described as:
["C]ells that fire together, wire together.” In other words, if things keep happening more or less simultaneously, you may assume that there is a common cause for the firing. More importantly, if one of the cell is active systematically just slightly before another, the firing of the first one might have a causal link to the firing of the second one and this causal link could be remembered by increasing the wiring of connections, a notion we call synaptic plasticity. In short, timing matters because it may indicate causality.
In other words, Hebbian learning is mediated by STDP. Thus STDP may explain how Hebbian learning may come to exist.
But Markram et al. caution:
...this is not to say that STDP has been a panacea for all problems
neuroscientific. Clearly cells that fire together wire together, there
is no doubt about that, so the coming of STDP has not rendered the
classical literature obsolete by any means.
In other words, Hebbian learning is more of a theoretical construct whereas STDP provides a neurophysiological explanation. Just like Mendel's ideas have been proven by the existence of DNA, and Darwin's ideas by a since buildup of fossil records, Hebbian learning has been explained by STDP, but that doesn't make Darwin nor Mendel's teachings obsolete.
- Dan & Poo, Neuron (2004); 44(1): 23-30
- Markram et al., Front Synaptic Neurosci (2012); 4: 2