Does effective theory have the same meaning in particle and condensed matter physics

I have a naive question about the meaning of effective theory in particle physics and condensed matter physics.

In particle physics, from what I know, the effective theory comes from the Wilsonian renormalization. We start from a theory with a fundamental cutoff $\Lambda$, e.g. Planck scale, and consider a smaller cutoff $\Lambda'$, e.g. LHC scale, $\Lambda'<\Lambda$. The Lagrangian then reshuffle into an infinity series including all possible powers of fields. The theory with $\Lambda'$ cutoff is called effective theory (possibly only a few leading terms)

In condensed matter theory, I heard the effective theory means neglect some details, like the BCS theory.

Roughly speaking, "the effective" in both fields has similar meaning, that we ignore something ($>\Lambda'$ in particle physics or uninteresting detail in condensend matter).

My question is, strictly speaking, does the two "effective" in particle and condensed physics have the same meaning? Can we start from QED, lower the cutoff, lead to BCS theory? (perhaps such crazy attempt will never work out...) or any deeper connection than heuristic similarities?

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In particle physics, the quantity deciding about the scale is roughly speaking $|p_\mu|$ – in the $c=1$ units, it doesn't matter which component of the energy-momentum we consider. In condensed matter physics, one must distinguish them because they don't obey $E\sim pc$ in general due to the breaking of relativity by the environment. The usual quantity deciding about the scale is the energy, not the momentum.