They're essentially the same thing.
If anything, the difference between them is similar to the difference between western cursive / print/ type writing.
Any person able to read japanese will comprehend and accept both writing styles as well.
A more "complete" explanation on the matter could probably be given to you by Toritoribe'san(japanese native) though.
Be aware that it isnt much of a big deal and should not hinder your progress studying!
I started out writing the first one when I was laboriously practicing my hiragana and ended up writing the second after a while, it's just quicker and easier. I don't really notice the difference when reading now.
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