The following is probably not entirely accurate, but I will try to highlight what I think the main differences are. Also, keep in mind that most of the names used above are umbrella terms for whole families of processes that might differ significantly within one family.
I think photogravure and circuit etching can be seen as somewhat similar with respect to the etching part: In both cases the metal is directly etched (i.e., one could say that the metal plate "holds the picture"), using for example ferric chloride. In some parts, the etching is moderated by some substance, for example by hardened gelatine in the case of photogravure. In circuit boards, this will leave the conductive tracks, in photogravures, these parts will hold less ink, thus appear as highlights in the print. Of course, for photogravure there is the preliminary step of contact-printing a picture onto the gelatin and the final step of making a print from the metal plate. From a "usability" point of view, photogravure requires already some sort of (positive) film created by another process and the aim is to obtain prints made with ink. For the wider family of processes, see also photoengraving and photolithography. The process predating daguerreotypes is heliography.
For tintypes, the metal plate only acts as a support/carrier for the photographic emulsion, which is collodion containing suspended silver halide. If glass is used instead of metal, you get an ambrotype. These plates are exposed directly in camera, then developed using a ferrous sulfate developer, and fixed using sodium thiosulfate (aka hypo) or potassium cyanide (warning: this last option is very dangerous!). They make a picture that appears as a positive (although, technically it is an underexposed negative). Both ambrotype and tintype belong to the family of collodion processes. This family also contains processes that are used to create actual negatives (i.e., ones used for making photographic prints) rather than positive-looking negatives.
For daguerreotypes, the metal plate is coated with a thin layer of silver, which is subsequently sensitized using halogen (or other) fumes. So one might say the metal plate also only acts as support/carrier, but the light sensitive material is more "closely" combined with the support, e.g. by electroplating. This plate is also directly exposed in camera and then developed using mercury fumes (please don't do this at home unless you really, really, really know what you're doing!) and fixed with sodium thiosulfate. The image appears positive or negative, depending on lighting and background.
So, tintypes and daguerreotypes are somewhat similar from the "usability" and "general process outline" point of view: In both cases, the metal plate is coated with a substance (collodion for tintypes and silver for daguerreotypes) that is then sensitized, exposed in camera, developed, and fixed. However, the (chemical) details are quite different, and to the best of my knowledge there is nothing like "cross-processing". However, there are many variants within the family of collodion processes, so a fair amount of experimentation is possible here.
Photogravure on the other hand, as outlined, is quite a different process with a different purpose: Here, you already need a (positive) image and the aim is to create a plate that can be used for intaglio printing.
Note that the collodion process is not too complicated to recreate at home and is reasonably safe when following the usual guidelines regarding safe handling of chemicals (and staying away from the potassium cyanide). This is not the case for daguerreotypes, they are quite complicated and very dangerous to create. If you intend to make daguerreotypes, it's best to do it under the guidance of an expert first, i.e., find a workshop or similar.
As others have pointed out, the Book of Alternative Photographics Processes by Christopher James is an excellent source for further information.
Finally, you can etch photographs into PCB boards, see for example here or here. Nothing stops you from using a plain photograph instead of a "meaningful" circuit. However, such a circuit board would most likely not be good for any electronics. If you want such a thing, you would need to do some conversion of the photograph first, e.g., akin to TSP Art, see also here (but of course with the aim of generating a meaningful circuit).