What is the difference between these two implementations?
If you check out what L.mapbox.map does internally, it adds a gridLayer and gridControl for the layer you specify. Basically the map constructor makes all of the safe assumptions it could make and does them automatically as a convenience.
Why is the tileLayer created using L.mapbox.tileLayer() different than the one created and automatically added using L.mapbox.map(3)?
It's the same - there's a gridLayer and gridControl in the mix when you use L.mapbox.map(3)
, and those are what make things interactive.
Are there plans to address this discontinuity in future changes to the API
It's not as much a discontinuity than an API design: we decided to keep tileLayers decoupled from gridLayers and gridControls so you can mix & match them - if you want to switch which layer interactive features come from, or disable interactivity without disabling the tile layer, you can.
will support for interactive tiles be dropped in TileMill 2?
No, you can use TileMill 2 and see how it supports interactivity. We aren't going to remove or phase this out, though vector tiles will have new methods of interaction.
For your second example, you would want something like:
var map = L.mapbox.map("map", "username.id2", {});
var gridLayer = L.mapbox.gridLayer("username.id1").addTo(map);
var gridControl = L.mapbox.gridControl(gridLayer).addTo(map);
map
.addLayer(L.mapbox.tileLayer("username.id1"), true)
.setView(L.latLng(61, -160.5), 4)
.setMaxBounds(L.latLngBounds(L.latLng(50,-180), L.latLng(72,-129)));