That would be because the SD card is considered "External" Storage while the phone's storage is "Internal" storage. So when you are looking at not having enough, you are looking at the "Internal" storage. You can free up space by moving files (not apps) to the card. Or you can look into making the card "Internal" storage (if possible on that device, as it isn't on all).
If you want to just move files (photos, videos, music, etc.), not apps, to the SD card you can use the file manager app that is on the device, or if there isn't one you can download and install one to access and move the files. Sadly, they usually only let you move one or two at a time.
To move them all at once, or in large amounts, you can connect the phone to a computer via USB cord, then move the files over to an empty folder on the computer. Once there, and still connected via USB, you can then move or copy the files over to the SD card. Personally I would suggest leaving a copy on the computer as a back up.
Once that is done you should then go into the apps that you access the files through (like gallery, etc.) and change the apps individual settings to look for the files on the SD card. You may also want to change the settings in apps that you use to create new files (like the camera) to save new ones to the card rather than the phone.
Now if you are wanting to move apps to the card, that is a whole other story.
First, you need to be using a phone that is running at least Android "Marshmallow" (or newer) or be able to upgrade to it. Second, you will need the instructions I am including below. And third, you need a phone that has not been restricted by the manufacturer from making this change. Which does happen.
NOTE: If any of the steps are missing on your phone, or they don't work for you, then you have a phone that either has an older Android version or has been restricted by the manufacturer.
How to turn the "External" SD card into "Internal" storage on "Marshmallow" a.k.a. 6.0.
NOTE: Please be sure you start with a blank SD card. It needs to be blank because when the card is converted to "Internal" storage, it will be formatted (wiped) and encoded (making the cards data only readable by that device).
1. Go to device “Settings”, then select “Storage”.
2. Select your "SD Card", then tap the “three-dot menu“ (top-right), now select “Settings” from in there.
3. Now select “Format as internal”, and then “Erase & Format”.
4. Your SD Card will now be formatted as internal storage.
5. Reboot your phone.
NOTE: If you don't reboot the phone, many things may not work correctly, so make sure you do.
How to turn the "External" SD card into "Internal" storage on "Nougat" a.k.a. 7.0.
IMPORTANT NOTE: Be sure you start with a blank SD card. When the card is converted to "Internal" storage, it will be formatted (wiped) and encoded (making the cards data only readable by that device), so anything on it prior would be gone.
1. Go to "Settings", and then select "Storage & USB".
2. At the bottom of the list you should see the SD card's details, including the option to format it and make it "Internal" storage.
3. Once this is done, reboot the device and you can start running things from the card.
If you don't reboot the phone, some things may not work correctly, so make sure you do the reboot.