Washington (CNN) Two very different types of crowds visited Washington in the past couple days -- one jubilantly cheering the swearing in of the 45th President of the United States, the other holding up signs that displayed messages like "Awful Man."

But there was one thing many of these individuals had in common: many, many brightly colored hats.

There is perhaps no other symbol that so encapsulates President Donald Trump's election than the bright red "Make America Great Again" hat, and they could be seen all over the city on the day of Trump's inauguration.

One day later, bright pink hats could be seen all over the city as people flocked for the Women's March as part of a grassroots movement to wear handmade, cat-eared knit hats, dubbed "pussyhats," in a show of solidarity and support for women's rights.

CNN spoke with the attendees of both crowds, asking what the hats meant to them and what they expected in the next four years of a Trump presidency.

What the hat means

"That's what Trump's known for, literally 'Make America Great Again,' Mackenzie Zipfel of Annapolis, Maryland, told CNN, pointing to the phrase emblazoned on her head. "And he wore it all the time, so I was just like what better way to support him than buy a hat?"

It was a message many other attendees echoed.

"It's Make America Great Again: We've been there before, we need to get back there again. We're optimistic, we're cautiously optimistic, and we're just looking forward to the new journey," Lynn Jones of Annandale, Virginia, told CNN.

However one attendee, a self-admitted Hillary Clinton voter, said he was there to witness a historic moment and bought the hat "mainly for the rain," Roger Weng of Los Angeles said with a laugh.

Leah Mooney of Coatesville, Pennsylania, told CNN her pink hat was a message of solidarity.

"It also goes back to his famous quote and that I don't even want to say," Mooney said, referencing vulgar comments Trump made in 2005 that surfaced during the election about grabbing a woman's genitals. "Objectify women, but we're going to stand up back to you."

A number of men were also spotted wearing the hat, including Robert Hampton of Indianapolis, Indiana.

"This isn't just a problem for women, this is a problem for everyone, we're all equal," he said.

Looking for unity

As attendees at the inauguration waited to enter security to the National Mall, many groups of protesters were also present, doing their best to send their own message.

"They need to give him a chance, because they really don't know anything, he hasn't even had a chance to do anything yet," Gabriella Zakrocki of Bel Air, Maryland, replied when asked what she'd say to them.

"I would say that they just need to look at the other side just like we did when Obama was becoming President," Craig Zawalich of Port Richie, Florida, told CNN. "I think if we just got along we could make things better, a better place for everybody, not just a certain crowd."

But marchers the next day were not ready to forget many of the issues that had turned them against Trump during the election.

"They're blind to a lot of the injustices that happen everyday," Washingtonian Willie Madien said.

"Get out of your state, meet new people, and look around -- everybody's working hard to make a buck and to get ahead," said Linda Greenwood of Huntington Woods, Michigan.

Looking for optimism

Unsurprisingly, many attendees at the inauguration were optimistic for the next four years under a Trump administration, but admitted there would be challenges.

"I feel it's going to be a challenge. I don't feel everything will be as smooth sailing as I think it's going -- as everybody would like it to be," Zawalich said. "I think there's going to be some backlash on things but I think we'll get through it and I think everything is going to work out and I think even the people who didn't support Trump are going to be very happy with the results."

Many attendees said their support for Trump was about a need for change, and they trusted Trump's ability to deliver.

But a day later, there was also some optimism for the future even as marchers bemoaned Trump's policies or tweets.

"I have to be optimistic that something good has to come from this. I mean, you have to have optimism to manifest into the universe and something good has to come," Pittsburgh resident Danielle Ivkovich said.

Emily Hardykarska of Lafayette, Indiana, said the huge crowds that turned out for the march invigorated her.

"People from all over the world here today, makes me a little emotional, but I know that I'm not alone, and none of us are alone and we can do so much together," she said.

"I keep trying to find the silver lining that he does have a message, he's got a plan, a solid plan. I haven't quite seen it. I don't want him to fail, because it's our country," Mooney said.

Bonnie Mitchell, a Washington resident, was on her way home after attending the march, pink hat still firmly on her head.

"I pray that the next four years will run smoothly for all," she said.