Same sound as 'sigh'?

[Torsten]

Hi, can you please help me understand the following two sentences? I mean, there are words that start with a silent 'h' and in my opinion and there are various ways of expressing or articulating a sigh.

The letter and sound ‘h’ is pronounced in words starting with ‘h’. This is the same sound as a sigh.

TOEIC listening, question-response: Which vendor do we use for break-room supplies?

[Mister Micawber]

I'm not sure quite what is being talked about, Torsten, but I suspect that it is words that start with a voiced /h/ but in unstressed syllables, as in 'Hawaiian' and 'historical'. It is a very weak /h/, and it does sound sort of like a sigh (a slightly voiced exhalation).
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Native English teacher at Mister Micawber's