I can answer part of your question.
Switching current/voltage - The voltage and current which the contacts can safely and reliably handle, and for which the relay was designed. For instance, you would not want to use a relay with 12 volt switching voltage to switch on/off a toaster running from 110 VAC.
max Contact rating - The maximum current and voltage which the contacts can handle. This varies from the previous rating because normal operation (the first rating) may be somewhat different from the extremes encountered. For instance, an automotive relay is generally described as a 12 volt relay. However, the actual voltages can be somewhat greater, particularly since a standard 12 volt lead-acid battery is normally charged to more than 13 volts.
Coil Voltage - the nominal voltage required across a coil to operate it. This may or may not be the same as the contact ratings.
Pickup Voltage - the coil voltage which is guaranteed to operate the relay from its no-voltage condition. Depending on the relay design, this is usually in the range of 80 to 90% of the nominal coil voltage.
And, just for completeness, there is Dropout Voltage, which is the complement of Pickup Voltage. For an activated relay, this is the voltage below which the relay is guaranteed to release. In some cases this may be as low as 15%.
And for the final question, I'm not psychic. How in the name of all that is holy do you think I could possibly know what relay is being referenced based on a bunch of pin numbers? And, for that matter, it's unlikely that a relay with a few pins (perhaps as few as 4) would have pin numbers as high as 87. More likely you are referring to the pins on a connector or terminal block. Without a schematic, there is simply no way to tell what you are talking about, and you need to understand this if you wish an answer to your questions.