Why does the checkout say my gift code is invalid?

Most often it went into the promo code box rather than the gift card box, or the card belongs to a different country's storefront.

Can I use a gift card and a discount code together?

Usually yes, because they do different jobs. The discount reduces the price and the gift card pays what is left.

Will the unspent part stay on the card?

Yes. Gift cards keep a running balance and you can come back to it, subject to the expiry in the terms.

How to use a gift card online

Where the field actually is

In rough order of how often each pattern appears:

On the payment step, as a collapsed link labelled Have a gift card? Easy to miss because it looks like small print.
On the basket page, next to the promo code box. These are two different boxes and putting a gift code in the promo box will fail.
In your account, under Gift cards or Wallet — you load the balance first, then it applies automatically at checkout.

That last pattern is common at large retailers and is the most reliable: load first, shop second.

Two boxes, two different things

The promo code box and the gift card box are not interchangeable. A promo code changes the price; a gift card pays the bill. Putting one in the other's box returns "invalid code", which people reasonably read as "my card is broken".

If a checkout shows only one box, look for the payment step. There is almost always a second one there.

When the basket costs more than the card

This is normal and every major checkout handles it. The gift card pays what it can and you pay the rest with a bank card. See how to split payment for the order of operations, which matters more than you would think.

When the basket costs less than the card

The leftover stays on the card. You are not obliged to spend it all, and no shop will offer you the difference in cash.

When there is no gift card field at all

Work through these:

You are not signed in. Many checkouts only show the field to account holders.
The basket contains something excluded. Other gift cards, marketplace items, subscriptions.
It is a delivery-only or collection-only flow with a cut-down checkout.
The card is in-store only. Less common now, still real.
Wrong region. The card belongs to another country's storefront.

Practical habits

Apply the gift card before choosing delivery, so you can see what you actually still owe.
Screenshot the confirmation if the balance was large. Disputes are much shorter with evidence.
Do not let a card sit at £2.30 because it is awkward. There are ways to spend a remainder.