My understanding of the IIIF Presentation APIs and TEI facsimiles is that the equivalences are:
- IIIF Collection = <tei:teiCorpus>
- IIIF Manifest = <tei:TEI> containing a <tei:facsimile>
- IIIF Canvas = <tei:surface> or <tei:surfaceGroup>
- A IIIF "Image annotation" on an IIIF Canvas = a <tei:graphic> element in a <tei:surface>.
- A IIIF Image annotation that refers to a sub-region of a Canvas = a <tei:graphic> inside a <tei:zone> which is inside a <tei:surface>. In IIIF the region of the annotation is given in a URI fragment identifier (e.g. #xywh=0,0,500,500); the corresponding <tei:zone> has attributes which specify a bounding box or polygon as a sequence of X,Y points.
- A IIIF annotation which isn't an image could correspond to various things in TEI: simple comments attached directly to an image would be modelled in TEI as <tei:desc> or <tei:label> elements within the <tei:surface> or <tei:zone>.
Slightly more complex is the notion of ordering:
- IIIF Sequences and Ranges model the logical ordering and arrangement of the Canvases. In TEI, the <tei:surface> elements obviously fall in an order in the XML file, but TEI users would usually consider that the logical arrangement of <tei:surface> elements is given by the logical order of the textual transcription, inside the tei:body element. In TEI, the <surface> elements are generally linked explicitly to <pb> (page break) elements in the TEI transcription. So in that sense, the TEI textual transcription really plays the role that Sequences and Ranges do in IIIF. The reason this is a complexity is that although the textual order of the content of a TEI transcription (the contents of a tei:body element) is generally just the order that the text appears in the file (so-called "document order"), this order can be modified; TEI has linking mechanisms (such as @next and @previous attributes) which can link parts of the text together in alternate orders, and logically join together segments of text that appear out of order. And there's also a "documentary" mode of analysis and transcription in TEI, in which the <facsimile> element contains the textual transcription. In this mode, there's no separate transcription in a <body> element; it is all embedded directly in the <facsimile>, <zone>, etc. markup; privileging the material aspect of the text over the logical aspect.
I hope that's helpful!
Might I ask, by the way, what use case you have in mind, particularly? Were you interested in making TEI texts that refer to IIIF services, or perhaps in making IIIF services which publish TEI texts? Or something else?
Personally I think the two models are conceptually very close and I can see possibilities for translation in both directions.