As far as relation between the Mac and IP address of a host is concerned, both donot have relations
but both are dependent on each other which depends on the situation.
Both are dependent on each other in case of ARP(Address Resolution Protocol) when an IP address
of a host(Computer or Router) is resolved to Mac address.
Mac(Media Access Control) is actually a physical address of a device which is constant and it
is used at a Data Link Layer of the OSI Model and IP address is an (Internet Protocol) address of a device which is used at Network Layer of OSI Model.
The layers of OSI reference model cannot function without the support of each other and since
the Network Layer is just above the Data Link Layer, if any one of these layers are not there than offcourse , the communication cannot take place .
Please note that IP address can be same or can be different depending on how you assign it.
I hope this answers your question and if you think this is still not clear then please donot hesitate to ask again.