Move application to external drive takes larger space than in the Macbook?

Moving Applications to an external drive is a Bad Idea®.

They lose the protection of the severely locked /Applications folder.

They lose the ability to be used as their own paging files when running, which means they use MUCH more RAM and paging space. They will run slower.

And lastly, as you have seen, using drive with a different format takes more space.

Move your User files, not Applications. Applications belong on the Boot drive.

<<They won't required more RAM to run nor security issues. >>

It is true that the storage needed to store the Application is no larger, but the issues I mentioned are much more complex than static storage.

Applications stored outside the /Applications folder require more space in RAM when running, for several reasons. When not protected in the /Applications folder, the system will not use the source file itself as an instant source for code pages. Instead, the entire Application needs to be copied into a temporary locked location to be run, sometimes called a "sandbox" file, and run from the (locked) Sandbox file instead of the original (easily re-writeable) application file.

The /Applications folder is locked, and MacOS allows no access to it without taking special care and requiring an Admin password to access it momentarily to place something new there. There is no such protection for applications stored outside the /Applications folder. Therefore, they may be more subject to attack by malware.

What format is the external drive and what applications are they?

Yes, likely so. APFS is very efficient in its storage abilities.