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Answers
They both lay eggs.
They both are colored black and white and orange. The Adelie penguin in the photo is only black and white, but the emperor penguin is black, white, and has orange stripes--one on either side of its bill.
They both fly and have wings. Well... the penguin "flies" underwater, and its wings are called flippers. It really does fly underwater... making the same flapping motions with its wings that birds do. And the flipper structure is the same as a bird's wing, although smaller because water is denser than air.
They both can navigate and migrate. The penguin travels north and south from its breeding colony to the wintering area in the pack ice. The monarch has a much longer migration to its wintering grounds, in Mexico. They both navigate using an internal clock (called "sun compass orientation").
They both are social--congregating in dense groups at times--the penguin in its breeding colony, the monarch in the oyamel trees of Mexico. Gatherings of each species can number as high as a million.
Both species are popular with people. Penguins are cute (because of erect posture), monarchs are beautiful.
Both have feathers and scales. Monarchs are covered with scales that act like miniature feathers, and in some places on the body have similar functions--such as providing color, warmth or streamlining. (But they aren't really feathers because they lack the interlocking parts.) Penguins have small and scaly feathers, different from most birds. Plus, they have real scales on their legs and feet.
Both hunker down and endure when the weather is stormy.
Both get tagged or banded, to study survival, migrations, and more.
Both have substantial claws. The penguin, 6, and the monarch, 8.
Both taste bad. I've tried penguins, and they taste fishy because... they eat fish. To stay underwater, their muscles have a dark, oxygen-storing pigment that makes the meat look black. Monarchs also taste bad, according to most birds. I haven't tried monarchs.
I could probably find other similarities (like basic biology or living on planet Earth), but I'm running out of good ideas.
Here's the really interesting part
Growth rate
Both are among the fastest growing animals known. The monarch caterpillar grows from a tiny hatchling to a large caterpillar 2,000 times larger in only two weeks. If a human baby grew that fast, it would be the size of an elephant in 14 days.
The Adelie penguin doesn't have a comparable rate of growth, but it's high up there for vertebrate animals. It has to grow so fast because in the Antarctic breeding area, the summer season is so short. Before winter slams down, the chicks have to grow fast, develop waterproof feathers, swim away, and start to feed themselves. Chicks ready for independence are actually a bit heavier than adults; they need the extra fat to tide them over till they become proficient at catching shrimp and fish.
Here's an example of how much penguin chicks eat, to grow so fast. I decided to raise two penguin chicks from eggs in my tiny field hut next to the penguin colony. I had a crate of frozen smelt (fish about 5-6" long) shipped all the way to Antarctica. Normally, parents return to feed their chicks every one or two days, so they have to eat a lot at one sitting.
When I fed one of the chicks, he ate about 30 smelt in a row. Then he settled back on his haunches with a huge stomach bulging out, rocked a bit trying to pack it all down with some odd motions, and burped. It reminds you of caterpillars, also specialized for eating lots and growing fast.
Both are ideal subjects for studying behavior
Caterpillars are docile, non-threatening, easy to raise, and easy to observe. They aren't afraid of you. With a large number of them munching away in a bin, you can see many different behaviors and adaptations all at once. In just over a month, you can observe their entire life cycle, then see it again several more times during a single summer. Their food costs nothing... easy to find. Equipment to raise them costs less than $20.
"No"...you say... "penguins can't be the same..." ??
I studied penguins for three summer seasons in the Antarctic for my Ph.D. thesis. The wonderful thing about penguins is that, like caterpillars, they aren't afraid of you. That's because there are no mammalian predators like bears or foxes on land in the Antarctic.
So, as you walk around the penguin colony, they just go about their business, paying no attention. That is, unless you invade their territory (about 3 feet in diameter,) or transgress their personal space. If that happens, they can be quite aggressive, whacking you with a hard, bony flipper moving like a fan blade. They can also peck with a sharp, hooked beak or scratch with their claws.
In the penguin colony, from one vantage point, you can see thousands of penguins all at once. Even very rare behaviors now become easy to see.
I have even seen penguin eggs explode with a loud bang. It took me quite a while to figure out what caused the noise. It's because penguin eggs have very thick shells--their nests are made of stones, after all. If the embryo in an egg dies and the adult continues to incubate it, the egg can become very rotten. Foul (fowl?) gasses build up until it explodes!
After several seasons in the Antarctic, I finally got to meet Dr. William Sladen, the first person to do a really scientific behavioral study of penguins in the wild. I was eager to share all the amazing things I had seen, like the disappearing eggs.
After listening to me politely, he said... "David, if you watch penguins long enough, you'll see almost anything." The same is true of caterpillars in a bin.
So why not get started... see how many caterpillar behaviors you can spot?
What about the cost of equipment to study penguins? One thing that's different: It's incredibly expensive to travel to Antarctica and to support people there. Your cold-weather gear has to be effective.
But most of the equipment needed for penguin study is basic. Binoculars, notebooks, plastic turkey bands with numbers, remolded to fit flippers, along with a hand-held fishing net to catch them. (When you need to get up close and personal.)
But I had trouble finding the right net. I needed a long-handled version of a net you'd use to land a trout when fishing. Long handled, because when you chase a penguin on land, they are very fast. Waddling? Not these. You are chasing them at a run and can't take the time to bend over if all you have is a short-handled net.
So, I'd go into a hardware store before leaving for the pole and ask: "Do you have a long-handled fishing net? "No, but we have a short-handled net...that will do the job for you." I'd explain that I really needed a long-handled one. Finally, they'd lose patience: "Well, what do you want to do with it?" I'd finally have to confess: "Catching penguins." The strange looks I got.
Another similarity: you catch both adult butterflies and penguins with a long-handled net. Both are pretty hard to catch.