[إشراق]

Ha agian Abu Elias

Ask whatever you are confused with English.

The members will help you as well as they can, and they will do all their best

Here you go the answer of your question

reserve = book but no check in

Reserve and book have the same meaning

you can say:
I'd like to reserve a room in the name of Elias

or you can say:
I'd like to book a room in the name of Elias

the difference as I thought is that

book : is especially used in British English

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check in:

the place where you show your ticket, or the place where you pay in the supermarket or hotel etc.

You cannot say:

I'd like to check in a room in the name of Elias

In this sentence you mean that:

You want to pay for the room which Elias booked or reserved.