A ‘Person’ is an individual while an ‘Organisation’ is a group of people which for instance represent a company.
The difference in AX is that dependent on this ‘Record type’ other fields become visible.
For example: When creating a ‘Person’, you can specify First and Last Name. In an ‘Organisation’ you’ll have Name.
(There’re more fields for both Record types).
Under the hood AX creates a entry in the Global Address Book called a Party.
Dependent of the Record Type you specify, the system uses another table (which inherits from the base Party table).
If you need more technical information, please ask.