In California the only thing a landlord needs to do in order to comply with the law if he wants someone to vacate one of his apartments/houses, is to give the renter a 30-day notice.
A 30-day notice is simply a landlord's polite way of saying I'd like you to vacate your apartment and you have 30 days in which to do it.
Same thing if YOU found another place and needed to move, you are required to give the landlord/manager a 30-day notice of your intention to vacate.
An eviction on the other hand is a little harsher, it's to expel a tenant from rented or leased land, building, etc., by legal process, like for example nonpayment of rent.
This would usually occur after all normal avenues to collect the rent have been exhausted...like the rent was not paid for the past month or two...depending on what the rent/lease agreement said.
In the case of an eviction, a Marshall might have to come by in order to comply with the legality of the tenant's removal and enforce the notice of eviction, a legal document.
If you had paid your rent on time and didn't break any rules and the landlord had reasons other than your failure to comply with his rules, then there's no reason you shouldn't get a good recommendation if a new, potential landlord calls him for a reference.