Abandon has many meanings. As a verb, means relinquishing control or residence over authority or placel. As a noun, if you say you are doing something with abandon, you are doing it without restraint, yielding to your impulses and instincts.
When you hike up Mount Snowdon, you'll find an abandoned hotel about three quarters of the way to the top. It dates from the early nineteenth century, and is very eerie.
A good singer performs with abandon, transforming himself or herself into something new and better in the process. No singer should be worried about anything, or even thinking, when performing.
Abandon ship is, literally, the order given by the captain to evacuate a sinking ship. Figuratively, abandon ship means pulling out of anything that is failing.
When the captain says "abandon ship," you know that things are serious. Either the ship is sinking or soon will be, so it's wise to do what he says.
As a company, Widgets, Inc., was not what it used to be. Many employees, sensing that things were getting worse, abandoned ship, seeking new jobs elsewhere. This only hastened the overall decline.
Giving up means surrendering someone or something. Give up can also mean to lose hope or admit defeat.
The police had the building surrounded, and helicopters were patrolling the air above. There was no way out, so the suspect finally gave himself up.
After spending eight years trying to get somewhere in the music business, I decided to give up and go to university. It wasn't much fun doing jobs I hated to support a music career that was going nowhere.
Another meaning for give up comes in the phrase give up the ghost, which means dying, sometimes literally but usually figuratively. If someone is pursuing something creative but is not especially talented, people might say don't give up your day job.
The company was struggling to keep up with a changing market, but eventually, the losses simply outweighed any gains they made. It quietly gave up the ghost in 2011.
I was busking in a park in Manchester, and several people would stop to listen. One of them sneered at me and told me not to give up my day job.