An in-house data centre need not have an automated resource provisioning and usage metering capability, utility fashion (i.e. for SaaS, automated provisioning and deployment of data sets into your application instance(s) and reporting on their usage by relevant metrics such as users or data throughput; for PaaS, automated provisioning and deployment of application components and instances thereof and their usage by relevant metrics such as messages processed or concurrent transactions; for IaaS, automated provisioning and deployment of virtual machines and their usage by relevant metrics such as CPU time or IOPS). It can be automated, it can be manual, or a combination of both.
A real private cloud does.
An in-house data centre is your facility, whether leased, built or bought.
A private cloud need not be. As long as only you are not sharing resources at the level being sold (e.g. for SaaS, nobody else is in your application instance; for PaaS, nobody else is processing transactions on the same transaction processor; for IaaS, nobody else is running VMs on the same physical hardware), you need not be the only customer in the facility/floor/room/cage/aisle/rack.
In short, an in-house data centre is not automatically a private cloud, nor is a private cloud automatically in an in-house data centre.