Hypervisor
Software that creates and manages virtual machines by allocating physical resources between them.
Type 1 (bare-metal) hypervisors like Proxmox VE and VMware ESXi run directly on hardware for maximum performance. Type 2 hypervisors like VirtualBox run on top of an existing OS. Proxmox is the most popular choice for homelabs because it combines VMs, containers and ZFS in one free platform.
For a homelab, a bare-metal hypervisor turns one physical machine into a flexible foundation you can carve into as many isolated systems as its resources allow. Features that matter in practice include snapshots (roll back a VM instantly after a bad change), backups (Proxmox integrates vzdump and Proxmox Backup Server), live migration in a cluster, and IOMMU-based passthrough so you can hand a GPU or disk controller directly to a VM. Since VMware ended its free tier, Proxmox has become the default for enthusiasts thanks to its cost, capability and large community.
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Virtual Machine(VM)
A software-based computer that runs its own operating system on top of physical hardware via a hypervisor.