No. Your affiliate link doesn't give new users a discount. It only tracks the referral so you get credit. Your affiliate code is what gives the discount.
What's the difference between my affiliate link and my affiliate code?
Affiliate link → tracks the referral so you get credit. No discount for the new user.
Affiliate code → entered at checkout. It gives the new customer a new customer discount and gives you credit.
Do people have to click my link to count as my referral?
No. They don't have to click your link at all. As long as your code is used at checkout, you get credit for the referral.
Which one should I share?
If you want your audience to save money, share your code, not just your link. You'll find both on your affiliate dashboard.