I'm doing an embedded-system project now. From my view, AT commands can be sent to a device to retrieve 4G information, dial and so on. On the other hand, we can also do that by calling APIs provided by the 4G vendor.
My question is what's the relationship between them? Is the API a wrapper for the AT commands?
Vendor's API (not only C, but also C++, Java or Python depending to the vendor and the modem model) can both be wrappers for AT commands and a wider, more powerful set of API were the user can port complex applications.
It depends on the vendor and on the model.
It is impossible to define a general "rule" about API provided by a Cellular Module (not necessarily a 4G module).
First of all every vendor usually implements standard AT Commands (both Hayes commands and extended standard commands for cellular devices). In the same way every vendor has it's own implementation of the user application area where the customers can store their own application to control the modem's functionalities and to use them according to their own application requirements.
AT commands remain the interface to be used when the modem needs to be connected (and driven) by an external host. When the user application area is used, instead, a wider set of API is usually provided. They may include:
The latter usually access a base layer involving all the functionalities provided by the modem. Usually this is the same layer invoked by the AT commands sent through modem's serial interface.
Of course it often happens that the library mentioned above provides just a subset of the functionalities usually exported with the AT commands set so, in order to "fill the gap", a further set of APIs is usually exported as well:
As an example, please check Telit Appzone here and here. It was the inspiration of my answer because I know it very well.