You could have a huge gas giant planet and a nickel-iron sphere of the exact same mass, although the latter would have a much smaller radius and therefore a much higher surface gravity, i.e., the surface would be closer to the center of mass.

The mass of the planet can be determined from Newton's laws, if we can measure the gravitational effect of the planet on its star. But I would imagine this would require some knowledge of how the orbital plane of the planet is oriented to our line of sight. The planet's gravity can cause a measurable shift in position of the star at right angles to the line of sight, and it can cause the planet to accelerate towards and away from us (measurable by Doppler shifts in the spectrum). Both of these shifts are used by planet hunters, but depending on how much the orbit is tilted relative to us, one effect will usually dominate over the other.