Hi Lawrence, let me explain to you using a story.
Imagine that I am creating a name list for people whom I will invite to my wedding ceremony. I scroll down my contact list on my smartphone and decide to invite Abel, Amy and Amir because they are my close friends. The next name that shows up is Brandon. We are mere acquaintances and he is known to be a jerk; therefore, I decide that I will NOT INCLUDE him in my list of invitees. I have just OMITTED him from my guest list.
I continue the process till I reach Zac, the last person in my contact list. I will definitely invite Zac, my high school buddy. Just as I was about to put my smartphone away, I suddenly remember that I know two Zacs -- Zac Sagan and Zac Stone. I have ACCIDENTALLY forgotten to include the latter. I have OMITTED Zac Stone UNINTENTIONALLY. How careless of me!
The next day, I run through my list once more and decide to remove some names because I can only invite 100 friends. My list contains 101 names. I decided to REMOVE a name that is ALREADY in my list -- Suzie. I'm sorry, Suzie. I will make up to you by inviting you to a private dinner at my home after my honeymoon!
As you can see:
Omit / Omitting / Omitted: To decide not to include something intentionally or unintentionally
Remove / Removing / Removed: To delete or take something away that is already there
I hope this helps you.