Local is probably similar to Gemma e4b you can get right now on Google Edge Gallery (the ios and Android app). Guessing that the more powerful version that will only work on the 12gb ram devices will be something unreleased that is similar but a bit larger

Google also awhile back announced being able to run full Gemini by leasing / renting hardware in your own datacenters so companies can train or access data without needing to send things to their datacenters. Nvidia based. Guessing Private Compute might just be Apple leasing a ton of those?