My question is whether a standard meter will register consumption no matter which side the source of power is on? As opposed to a net or bi directional meter that knows the difference? For example, if the solar is out producing the loads in a home and the standard meter is still installed, will it register as consumption?
By the simplest design possible, a meter would function as a net meter. It would spin forward, or spin backward, depending on the instantaneous direction of net power flow.
Making the meter anything other than a net meter, is a countermeasure to tampering and unauthorized generation. It is common for such a meter to either register exported power as consumed power (called secure-forward), or it might just ignore exported power and count its energy as zero.
The term net meter means it treats all kW-hrs equally, and credits you fully for what you export. It adds to the total during instants when you import, and subtracts from the total during periods when you export.
The term bidirectional meter means it has two separate registers for import and export. You may have different rates applied to each one, such that it is likely in your interest to self-consume, instead of export.
In any case, no meter can tell the difference between 1 kW consumed, vs 11 kW consumed simultaneously with 10 kW produced. All it can track is net power flow (instantaneous consumption minus production), and the corresponding energy that accumulates with time. Graph net power vs time. Shade the area between the positive part of the curve and the time-axis blue, and likewise red for the negative part of the curve. Bidirectional means it tracks red and blue area separately. Net means it subtracts red from blue. Secure-forward means it tracks both red and blue together as if they were both positive, ignoring the fact that red is negative.