Multi-tier and/or ditstributed apps, do they have the same meaning ?
When we talk about layers in these apps, is it physical layers (database, browser, web server,...) or logical layers (data access layer, business layer,...) ?
Maybe these two sentences do convey intuitively the distinction between distributed and multi-tier:
In one case, the same processing is replicated over several nodes. In the other case, each tier has a distinct responsibility and the processing running on each tier differ.
Both notions are not exclusive: you can have non-distributed multi-tier apps (if there is no form of redundancy/replication), distributed apps which are not multi-tier, but also multi-tier apps which are distributed (if they have some form of redundancy).
There would be a lot more to say about the distinction, but the difference (to me) is essentially there.