Search is something you have more control over. The better your keywords, the better your chances of being found.
Suggested is largely up to the audience. The algorithm follows the audience, so if your videos align with what the audience wants to see, it will be suggested to them.
But you definitely have more control over search. Not guaranteed, but you can craft your search results over time, suggested is much more challenging (in my opinion) but very powerful once you get suggested.
you can help it a bit with suggesting your own videos in your description, pinned comment and most importantly, end screen cards, and those will help slowly push your suggested videos out more and more over time.