Question

1. I called him, but he did not hear me.
2. And a month ago, I needed him and I called him.
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Does 'I called him' mean 'I made a telephone call to him' or not?

Or does it mean the following?
"to utter in a loud distinct voice —often used with out"

Answer 1

In sentence 1, because of "he did not hear me," I'd take it that I yelled -- not on the phone.

In sentence 2, the calling could mean yelling or called on the phone.

My mother called me for dinner.
(She used a loud voice; she yelled; she hollered ... )

My mother, who lives in California, called me the other night, and we talked for over an hour!
(She called me on the phone, but not in a loud voice!)