Hi,
Note that for the shipping method selection to appear on the checkout, you need to have the "shipping" block in the "checkout workflow" setting of the HikaShop configuration. If you've removed it from there, then you won't have the shipping method selection, and you'll only see the automatically pre selecter shipping method in the cart, without a way of changing it.
So it could be the reason you're saying you're not seeing both.
Another reason could be with the settings of the shipping method.
Could you provide a screenshot of the settings of the shipping method which doesn't appear on your checkout ?
Also, in each product, in the "shipping prices" section, if you check the "block" checkbox of a shipping method, if the product is in the cart, then the shipping method won't appear. So it could also be a reason for it.