I'm a Japanese student studying English.

Do the following sentences have the same meaning?

Linda had three times as many pens as I did.

Linda had three times more pens than I did.

I think the former means Linda had 30 pens if I had 10

and the latter, Linda had 40 if I had 10,

but a lot of native speakers say there's no difference,

Then how about the followings?

Linda had half as many pens as I did.

Linda had half more pens than I did.

In this case, I think the former means Linda had 5 pens if I had 10

and the latter means Linda had 15 if I had 10,

and this difference appears clearer than the upper one.

What do you native users of English think?