Conventional Hayes and Hayes Compatible modems are all wired identically. These devices are classified as DCE (Data Communications Equipment). In general they have a DB25s (Female) interface connector pinned as follows:
|2||Recv'd data||Input to modem|
|3||Xmit'd data||Output to DTE device (PC/denso)|
|4||Request to send||Input from DTE... PC is ready!|
|5||Clear to send||Output to DTE... channel ready|
|6||Data set ready||Output to DTE... channel ready|
|8||Carrier Detect||Output to DTE... channel ready|
|11||Alert Plus||Output to DTE...|
|20||Data Terminal Ready||Input from DTE... PC is ready!|
|22||Ring Indicator||Output to DTE... line status|
The RS232 standard describes two different device types;  devices that originate information (DTE), and  devices that simply pass that information along (DCE). No other decision has resulted in so much confusion. The RS232 specifications resulted in two differing wiring schemes.
In the minds of the creators, a DTE would always interface to a DCE. Thus with the paired wiring schemes, interconnection would always be via a straight, pin-to-pin cable.
Over the years hundreds of devices have been developed with RS232 communications abilities. For example both computers (and X-Rite densitometers) are classified as DTE (Data Terminal Equipment).
It has been pretty much the choice of the manufacturer as to which of the wiring schemes to adopt. Thus it is generally anything but simple to ascertain the correct wiring.