This is an interesting question. Basically it's very similar like any meteorite collision. The gas planet makes here no other difference, but that there will be no crater.
Assuming a Jupiter-like planet and an Earth-like planet (Except,
say... half the mass of Jupiter), what would happen when the two
collide? For clarification: What would the actual collision be like?
The mass is only a part of the story, the collision velocity has much greater influence as the Kinetic energy is $1/2mv^2$, and at collision this all will be transferred to pressure, and then agin to kinetic energy. If this new kinetic energy is above the escape velocity, then there will be a truly "explosion" which causes the planets to be broken and lost material in the space. If this velocity can't be reached, then the collision will be very similar like an elastic collision.
Here on earth solids always just travel through gases "easily" (with some friction). Would the solid planet similarly just pass into the gas planet?
No, The friction based burning of meteorites, changes nothing in the fact that the entering in the atmosphere causes pressure waves. Even though these pressure waves travels oft behind the meteorite, similarily like the sound waves behind hypersonic airplane. But as long these pressure waves doesn't produce escape velocity, the collision will be very similar to elastic collision.
Let's calculate something. But please note that the velocity is a really important factor here.
If 1/2 Jupiter would be collided by the mass of Earth?
- The collision would be perpendicular to the travel direction of 1/2 Jupiter
- The velocity of the colliding "Earth" would be same as orbiting Earth; 30 km/s
- The escape velocity of "1/2 Jupiter" is 0.707 x Jupiter; 42 km/s
As the collision velocity is allready smaller than the escape velocity, there is no mechanism which could produce an "explosion" which would lead to a significant material loss; some amount of gases of the upper atmosphere of "1/2 Jupiter" will be blown away, but the collision is mostly absorbed. It's not even possible that the Earth shoots through the "1/2 Jupiter" as, the velocity is not enough for that even in entrance.
Note that the result of this collision would change if the the planets make a frontal collision; The orbital speed of Jupiter is 13 km/s, und thus such a collision would be able to produce escape velocities to "1/2 Jupiter", but not to Jupiter.
Would the answer to this question change if both planets had Earth-like masses?
Yes, This really makes a difference. The escape velocity of Earth is only 11.2 km/s, so the collision would produce velocities able to escape the gravity. And it might be even possible that the Earth would shoot through this "gas mass earth". Let's calculate.
If this Gas Earth would had similar density as Jupiter; 1/4, it's volume is 4 x time's bigger and radius is thus 1.6 x times bigger then that of normal Earth. This means that the Earth would collide only to a "fluid cylinder" with length of 3.2 and diameter of 2 Earth radius. Thus The Earth would collide only to a part of it's mass. The Result would be that the Solid earth would go through with reduced velocity and the gas planet would mostly explode, but some of it's mass would be catched by the solid earth.