First, storage options:
In the past, hard drives used spinning magnetic disks as storage. The full technical name is HDD, Hard Disk Drive. But we called this hard drive, for short.
Today, rather than a spinning magnetic disk, the best computers use flash memory. One of the many advantages of flash memory is that it has no moving parts - indeed it's all a chip. Thus, the technical name is SSD, Solid State Drive.
However, for short, many people will still call this a hard drive because the end-user uses both in the same way, so the difference is immaterial and the specifics can be gleaned from context.
SSDs and HDDs both store the operating system, the applications, and all the files you have. SSDs are also faster than HDDs, use less energy, can be much smaller, lighter, and thinner, are typically less prone to physical damage, and generally tend to have a lower failure rate. They are overall pretty great. The new Macbook has one of the fastest SSDs available.
Apple called it "PCIe-based onboard flash storage" for a few reasons. It's PCIe-based as opposed to SATA-based, which was an older and slower protocol. It's onboard, meaning it cannot be upgraded after purchase (this is important). It's flash storage, which means it's an SSD, not sure why Apple prefers one term of the other.
Second, which model you should get:
The first choice really comes down to storage. Since it cannot be upgraded post-purchase, chose wisely. Your only choices are 256GB or 512GB.
Take stock of what files you have today. How many photos do you have? How much music do you have? How many movies do you have? What is the size of your home directory?
Since you said you mostly use it for writing, I bet 256GB is enough. If you have the cash, 512GB would give you much more room to grow.
The second choice is about processor, whether to upgrade to the 1.3ghz processor. I would say it's not worth it. Benchmarks show the improvement is rather minimal. If it was $50-$100 extra, I would. Seeing how it's a $250 extra on the 256GB model, and $150 extra on the 512GB model, I wouldn't do it unless money was was abundant.
In the end, if you're the type of user that would notice the speed difference, odds are the Macbook Pro is really the computer you should be buying.
Third, consider the Macbook Air:
It has better battery life, it's more powerful with more options, for less money. It's a bit thicker (though still very thin), a bit heavier (though still very light), and has a non-Retina screen (the screen is average overall).
