Goin a bit deep...

Let's say a the Font Catull used in Google's logo, There's a website which previews the selected words of that font. What I'm saying is, is it illegal to snap the picture and recreate the gylphs and use it for my own use or give it away. Like tracing thing, is it considered illegal or it's okay to do that?

Thanks for taking your time

No that is not okay. Unless of course when you consider stealing okay

It's (probably) not illegal.

If you do it in the manner you describe, you are not using the Font Software, which would be copyrighted.

You also shouldn't even mention the name "Catull" anywhere, because that is trademarked.

The typeface, i.e. the style of the glyphs, could be design patented, but a) I doubt that Catull is and b) this has never been tried in court. Despite the myriad of obvious plagiarisms of popular typefaces.
Because it would be a mess.

Arial and Helvetica are very close. There are diffences though. Now someone needs to define how many differences a font would need to be considered disinct? Does every letter have to show some distinction? If so, how many variations of 'o' can there realisitically be? But if not all letters must be distinct, how many can be the same - 10, 20?
And what is distinct? Can I just take a typeface and change its width to 99%? Can I just in-/decrease the font weight by 2%?

Once design patents on fonts start being enforced, the life of font designers would turn to hell. Because they're all just producing minor variations of the same Latin Alphabet. It would be next to impossible to create a new text typeface and not run into infringement problems.
And nobody wants that.

Thus, nobody has ever been sued over plagiarising a typeface. The only court cases I'm aware of were against companies who used the Font Software, ie. the .ttf of .eot or whatever, which is an obvious copyright violation.

Everything else is just FUD by font designers.