Learn English – the sun shone or the sun was shining

If the action of the story is taking place the morning after the rain, you should use "it had rained". If the action of the story takes place on the night of the rain, you should use "it was raining".

Variants of this question have been asked here on ELL many times (for recent examples, see here, here, here, and here). But I really like how you added this detail, because it helps explain your conundrum:

I am learning past progressive right now and my brain is telling me that it must be different; otherwise, why have simple past and past progressive?

So, let's look at your two sentences:

I was walking to the park.
I walked to the park.

They are both very similar. They both indicate a walk to the park, a walk that happened in the past. In that sense, they don't really "mean" anything different.

So, why have both tenses? That's because of context. Very few English speakers utter simple sentences like "I walked to the park," or, "It was raining," or, "I saw a dog," unless we are answering a question, or telling a story and furnishing additional information. That's why it's so hard to analyze two simple sentences in isolation and figure out some subtle difference in meaning. Taken by themselves, the sentences don't really have a difference in meaning, they just have a difference in how they get used.

Let's imagine a family sitting around a dinner table. Someone asks:

Did anyone walk the dog yesterday?

I might answer:

I walked the dog.

I wouldn't say, "I was walking the dog," because there was nothing else going on, and there's nothing else to say. The dog and I both got our exercise. That's it. Simple past.

However, let's say someone asks a different question:

Is it true that you saw that car accident yesterday? What happened?

Now there's a question that's asking for a story! So, I might begin:

I was walking the dog when I suddenly heard some tires squeal. This old, blue car came
tearing down the street! It careened out of control, and then smashed into three or four
other cars. Glass was shattered everywhere.

In this case, that bit about me walking the dog merely sets up the story. It explains why I happened to be an eyewitness to the dramatic accident. That part would sound very out of place if I used the simple past when describing the walk with the dog:

I walked the dog. Suddenly, I heard some tires squeal. An old, blue car came tearing down the street!

(In fact, that version of the story makes it sound like I may have seen the accident after my walk, not during. It doesn't fit well with the story.)

Of course, there are many different ways I could begin this story, not just one. In fact, I might begin my narrative a bit differently every time I was asked to recount the details:

• I was out walking my dog on the sidewalk when I suddenly heard some tires squeal.
• I was in the middle of my walk with the dog when I suddenly heard some tires squeal.

Notice how I'm sneaking in some additional information with these two versions. The first one indicates that at least some of the streets in my neighborhood have sidewalks. The second one suggests that, if my usual walk is an out-and-back, I was somewhere near my turnaround point when I witnessed the accident.

But don't let those little details get in the way of my main point: When you just look at two sentences – one in the simple past, the other in the past progressive – don't search for some difference in meaning. You'll drive yourself crazy. Instead, try to imagine situations where one would be more appropriate than the other:

Where did you go yesterday?
I walked to the park.

Where were you yesterday, around noon, when I tried to call you?
I was walking to the park.