It depends on the letter(s) after GW.
A 1GWe plant produces 1GW of electrical power. At 20% efficiency, it will have to get rid of 4 GW heat.
You will sometimes see 1GWth - that produces 1GW of thermal power; as you have told us its efficiency is 20%, it'll produce 200MW electrical power (200MWe).
But no practical thermal plant of that size will have efficiency below 30% - some (like AGR) are around 40% as opposed to PWR in the 30-35% range, and CCGT can easily exceed 50%.
Without a suffix, you can assume it's rated by its electrical output.
Solar power is rated a little differently, but again its rating is its electrical output under optimum conditions, so a 1 GW plant (with 20% efficient solar cells) is intercepting 5GW of sunlight and producing 1 GW of power. That means, 200GW capacity will produce 200GWh in one really good hour.
But that's not the whole story, because that 200GW capacity doesn't reflect the power you'll get all day every day. Factoring in night-time, cloudy days, weaker morning and evening sunshine etc, a solar plant may only operate at something like 20% of its actual capacity, averaged throughout the whole year.
And I have to wonder if this (more properly called 20% "availability" or "capacity factor" as pjc50 says) is what your "20% efficiency" is really referring to? I suspect it is.
This means that a country with a 200GW power demand cannot meet it with a 200GW solar installation alone.
Grid planning is a fascinating problem anyway thanks to demand variability during the day; adding variable supply to the mix doesn't fundamentally change this but modifies the constraints. Currently, solar (in the UK) is helping, as peak sunlight coincides with daytime demand, leaving two smaller peaks morning and evening, doubling the value of storage (pumped hydro storage, and batteries in future).
More advanced solar users (Germany) sometimes see the daytime spot price go negative, as supply exceeds demand. This is more of an opportunity than a problem ... watch solutions emerge (not only storage, but also time-shifting big loads) to utilise a free or negative price resource.
Now, what can we get from your numbers?
1000 billion units (kWh) = 10^12 kWh over 8000 hours (a very approximate year!) gives us a mean demand of 10^12/8 W = 120GW.
Demand will be lower at night and higher during the day - say, 80GW and 160GW respectively. Therefore there is enough solar capacity alone to exceed likely daytime demand during (probably rare) peak solar periods.
There will normally be some storage capacity to consume some of the excess, helping fill the morning/evening demand peaks, and some other renewable power generation (wind, hydro) to cover part of the night demand. And probably thermal generation to fill in otherwise.
Best case : assuming enough storage to consume peak solar... solar provides 200GW * 20% capacity factor * 8000 hours = 320 billion units or 32% of your annual demand.
Close to worst case : assume half the operating hours are limited by demand to 160GW, so 80% of nameplate capacity. One way to account for this would be factor this in to the capacity factor as (10% + (10% * 0.8)) = 18% capacity factor.
Then solar provides 200GW * 18% capacity factor * 8000 hours = 288 billion units or 29% of your annual demand.
Better inputs (like actual demand curves, storage capacity, and knowledge of other sources) will refine these crude estimates, of course. But hopefully this is good enough to get you started.
You can make some conclusions even from a simple analysis like this : for example, if you have this much solar power, you need charging points wherever you park your car during daylight hours. Which means, for many people, at the workplace.
