  The BL Lac object 1ES 0647+250 is one of the few distant $\gamma$-ray
emitting blazars detected at very high energies (VHE, $\gtrsim$100 GeV) during
a non-flaring state. It was detected with the MAGIC telescopes during its low
activity in the years 2009-2011, as well as during three flaring activities in
the years 2014, 2019 and 2020, with the highest VHE flux in the latter epoch.
An extensive multi-instrument data set was collected within several coordinated
observing campaigns throughout these years. We aim to characterise the
long-term multi-band flux variability of 1ES 0647+250, as well as its broadband
spectral energy distribution (SED) during four distinct activity states
selected in four different epochs, in order to constrain the physical
parameters of the blazar emission region under certain assumptions. We evaluate
the variability and correlation of the emission in the different energy bands
with the fractional variability and the Z-transformed Discrete Correlation
Function, as well as its spectral evolution in X-rays and $\gamma$ rays. Owing
to the controversy in the redshift measurements of 1ES 0647+250 reported in the
literature, we also estimate its distance in an indirect manner through the
comparison of the GeV and TeV spectra from simultaneous observations with
Fermi-LAT and MAGIC during the strongest flaring activity detected to date.
Moreover, we interpret the SEDs from the four distinct activity states within
the framework of one-component and two-component leptonic models, proposing
specific scenarios that are able to reproduce the available multi-instrument
data.
