1. Eq. (1) is a passive general coordinate transformation of a scalar in GR, or is an active Lorentz transformation of a scalar in SR, while eq. (2.121) is an active scale transformation.

2. An active infinitesimal diffeomorphism generated by a vector field $X$ of a scalar $\phi$ in GR satisfy $${\cal L}_X\phi = X[\phi].$$

1. Eq. (1) is a passive general coordinate transformation of a scalar in GR, or is an active Lorentz transformation of a scalar in SR.

2. In contrast, an active infinitesimal diffeomorphism generated by a vector field $X$ of a scalar $\phi$ in GR satisfies $${\cal L}_X\phi = X[\phi].$$

3. Eq. (2.121) is an active scale transformation.

Hint: Eq. (1) is a passive coordinate transformation of a scalar, while eq. (2.121) is an active scale transformation.

1. Eq. (1) is a passive general coordinate transformation of a scalar in GR, or is an active Lorentz transformation of a scalar in SR, while eq. (2.121) is an active scale transformation.

2. An active infinitesimal diffeomorphism generated by a vector field $X$ of a scalar $\phi$ in GR satisfy $${\cal L}_X\phi = X[\phi].$$