MC v1.20.1

ContainerItemHandler.java

protected static class ContainerItemHandler implements Container {
    @NonNull
    IItemHandler itemHandler;

    @Setter
    @Nullable
    IChangeHandler changeHandler;

    public ContainerHandler(@NonNull IItemHandler handler, @NonNull IChangeHandler changeHandler) {
        this.itemHandler = handler;
        this.changeHandler = changeHandler;
    }
    private ContainerHandler(@NonNull IItemHandler handler) {
        this(handler, null);
    }

    @Override
    public int getContainerSize() {
        return itemHandler.getSlots();
    }

    @Override
    public boolean isEmpty() {
        for (int i = 0; i < this.getContainerSize(); i++) {
            if (!itemHandler.getStackInSlot(i).isEmpty()) {
                return false;
            }
        }
        return true;
    }

    @Override
    public ItemStack getItem(int pSlot) {
        return itemHandler.getStackInSlot(pSlot);
    }

    @Override
    public ItemStack removeItem(int pSlot, int pAmount) {
        return itemHandler.extractItem(pSlot, pAmount, false);
    }

    @Override
    public ItemStack removeItemNoUpdate(int pSlot) {
        return itemHandler.getStackInSlot(pSlot).copyAndClear();
    }

    @Override
    public void setItem(int pSlot, ItemStack pStack) {
        itemHandler.getStackInSlot(pSlot).setCount(0);
        itemHandler.insertItem(pSlot, pStack, false);
    }

    @Override
    public void setChanged() {
        if (this.changeHandler != null) this.changeHandler.onChange();
    }

    @Override
    public boolean stillValid(Player pPlayer) {
        return true; // IItemHandler is always valid, so Container is as well.
    }

    @Override
    public void clearContent() {
        for (int i = 0; i < this.getContainerSize(); i++) {
            itemHandler.getStackInSlot(i).setCount(0);
        }
    }
}

Details.md

Container is a superset of IItemHandler - almost every Container (GUI with slots) in both modded and vanilla can "handle items". And example of a block which is a Container but isn't an IItemHandler would be a liquid tank which has a GUI showing how full it is but doesn't have item slots (i.e. accept buckets).