The TESS file format is described in Section 2.1 of the TESS Science Data Products Description Document (data at the major archives such as MAST, IPAC/NEXSci or PDS should always have one of these data product documents that describe the data format, contents and issues or gotchas and so they are well worth hunting down first). That section breaks down and explains the format for all the TESS data products, not just the Full Frame Images. For the _ffic files, which you correctly guessed are calibrated fullframe images, we have (quotes from the document in quotation marks):
tess<yyyydddhhmmss>-s<sctr>-<cam>-<ccd>-<scid>-<cr>_ffic.fits.gz
where:
<yyyydddhhmmss> is an UTC timestamp which Section 2.4.1 says "is usually the start of the spacecraft pointing time".<sctr> is indeed the sector number (with a s prefix), which "is a 4 digit zero-padded integer indicating the sector in which the data were collected"<cam> is a single digit that camera number which can be "1", "2", "3", or "4".<ccd>, is a single digit that identifies CCD chip and can also be one of "1", "2", "3", or "4".<scid> "is a four digit zero padded identifier of the spacecraft configuration map used to process this data." (I wouldn't worry about this one, it probably only means something to the engineers...)<cr>, refers to the cosmic ray mitigation performed. Quoting "The value of this file name parameter will be 'x' if no mitigation at the SPOC (Science Processing Operations Center) was performed, 's' when mitigation
was performed on the spacecraft, the value will be 'a' to indicate that a SPOC mitigation algorithm was used, and 'b' to indicate that both the SPOC algorithm and the the spacecraft algorithm was used."
The other possible data types such as the target pixel data, light curves etc are also described in the Table 1. The document then goes onto to describe each product in more detail, starting with Full Frame Images in Section 3.
