Normally, the universities issue multiple transcripts to students when needed. Same goes with the TOEFL or IELTS results if requested. Those are sent to universities/authorities and not returned.
I understand the situation was different for government run Pakistani universities. They would not issue more than one and if they did, it was a cumbersome process.
As KakaBalli said thats what universities require, generally in my case the school had directly sent transcripts to the other institution or in one case i actually got it re issued and sent it to them, with that said yes i believe it is general practice in North America atleast, i am not too certain about Asia that much.
Transcripts and Test results are commonly requested by institutions and even some employers to be directly sent from the granting institutions. As an applicant, you're often required to contact your credential granting institution to request transcripts to be sent directly to the institution you're applying to (usually a small fee is required).