I used to think 'call a taxi' means calling a taxi using phone or cell phone app. On the other hand, on the street, it seems I have to hail a taxi than call a taxi. Is this suitable usage?
Technically yes, you're right. Hailing a taxi involves standing on the street and trying to get their attention with your arms or similar. Calling a taxi probably involves using a phone (though if there was a taxi rank nearby that you could call out - i.e. shout - to, that would be a suitable use of the phrase too).
That said, "hailing" is a fairly specific word that not everyone uses. If someone uses "call a taxi", I wouldn't be surprised if they then go and hail a taxi. So if (for some reason) you need to be absolutely explicit that you are using a phone instead of going onto the street, you'll need to make this clear (e.g. "I don't think I'll have much luck hailing a taxi at this time, I'll call one instead").
Colloquially, you're likely to hear any number of acquire-type verbs used to refer to making a taxi turn up: "I'll get us a taxi", "I'll grab us a taxi", "I'll summon a taxi", etc. These definitely don't say anything about the method used, and just refer to the result.