I've always had a bit of fuzziness concerning relativistic contraction which I will try to put into words.
Iiuc in SR, moving objects contract in the direction of their travel, as measured by rulers at rest w.r.t. said objects. A traveling ruler when compared to the static one will appear shorter, and if we imagine a set of clocks in the moving frame spaced 1m apart in that frame, they will appear closer together in the rest frame. Thus in SR objects contract and if we take the spaced clocks as a metric then the moving frame is entirely contracted as well. To observers traveling in the moving frame however everything appears 'normal', with no contraction.
But in GR iiuc it is only space, and not objects, that contracts in the presence of a $g$-field. A ruler in the presence of (for instance) a constant $g$-field will not contract as compared to the same ruler when not in the $g$-field. But a set of meter-spaced clocks in a region of no $g$-field, will be closer together when in the presence of a $g$-field, as measured by the (non-contracting) ruler in the same g-field.
If objects were also contracted in GR, then (for instance) its hard for me to understand how LIGO could work, since the light between the mirrors would get squished just as much as the space between the mirrors was squished, and you wouldn't be able to measure any effect.
Have I got this right?