Internal storage can be used for any mixture of media, apps and app data. Removable SD cards are different: by default SD cards are used in Android for media storage, not apps. So just putting a card in will make no difference to your app storage.
There are, as
@ocnbrze says, two ways of using the sd card for apps (3 if you are prepared to root your phone, i.e. modify your phone's firmware, but as that's something for enthusiasts, and has cons as well as pros which you should understand before considering it, let's leave that for now). Neither is guaranteed to be available to you:
* If you just use the card "as is" you may be able to partially move apps to SD. Go into your Settings > Apps, select an app you installed (not a pre-installed one), and see whether you have a "move to SD" button. Not all apps allow this, but if your phone supports it then the button should be there, though will be greyed-out if the app doesn't allow it. If it's there you can use it to move part of the app to SD - but don't do this with apps whose widgets you use, as they will stop working on your next reboot. If none of your apps have such a button this means that your phone software does not support this option (most do, but not all).
* The other option is to format the card as "internal" storage. If you do this then it will behave exactly like internal storage, both in that it can be used for apps and their data and also in that you can't use it in another device (as it will be encrypted). The pro is it gives you more flexible storage, the con is that it can't be used in another phone without reformatting (which erases everything on it, so back up before doing this) and it will be a little slower than the phone's internal storage (and SD cards wear out faster). Again, not all phones support this, with some brands particularly removing the option from their flagships. If your phone has the option you'll find it in Settings > Storage.
