Grandma's Pearls - are they real?

These were my dear Grandmother's pearls. I love them because I loved her, and I'm not concerned about monetary value. That said, I'm curious about whether they're real, and whether there's anything I should know about caring for them. Does the shorter strand need to be re-strung, for example?

The shorter strand is a creamier color, larger pearls, and more loosely knotted (pearls farther apart). The longer strand has a slightly darker color, smaller pearls, and more tightly knotted.

Can anyone help me learn more about what I have here?

The shorter strand appears to be akoya pearls. They need to be restrung; old, grimy silk can break.
Many of us do this for ourselves; it's not hard and saves money. I posted a tutorial on the Lowly Beader's Club section of this forum -- you can find it stickied there, and there are also some DIY stringing videos.

The longer strand, I'm on the fence about from the photos. They could be akoyas or they could be imitations.
Do these 2 tests, testing the short strand first so you know what real pearls feel like.

1. For each strand, rub 2 of the pearls together, gently. Real pearls feel a bit gritty when rubbed together; imitation pearls glide smoothly.
What do you feel with the short strand, and how does that compare with how you feel when you test the long strand?

2. Real pearls feel cooler than fake pearls. If both strands have been in the same room for half an hour or so (to eliminate that variable), touch each strand briefly to your lips. Lips are very sensitive to temperature. Do the strands feel like the same temperature or is the short strand cooler than the long strand?

Thank you so much, Pearl Dreams! This is super helpful. For test #2, they both seem like the same temperature. For test #1, I *think* the grittiness is similar, but I'm not 100% confident that I can tell.

The clasps appear to be identical (although the clasp on the shorter strand is tarnished). If you're fairly certain that the shorter strand are akoya pearls, would the identical clasps suggest that they were purchased together and maybe they are both akoya?

That makes sense to me.

Here is the tutorial:

As far as caring for them:

Store them apart from jewelry that can scratch them.
Pearls should be the last thing you put on and the first thing you take off.
Don't expose them to perfumes and hair products.
After wearing them, wipe them with a soft cloth (microfiber is great) before putting them away. If it's been an especially hot, sweaty day, dampen the cloth.
And restring periodically. If the thread becomes grimy or gaps appear, it is time to restring.