A patch file is a recipe, not a game. I group the formats this site can apply by how they fail when the base file is wrong. IPS and EBP overwrite bytes and will still produce an output if the base is the wrong revision. BPS and UPS refuse to continue when the source checksum does not match. xdelta sits in between: the window may carry an Adler-32, and this browser build checks a target checksum only when it can predict the output size.
IPS starts with the five bytes PATCH and stops at EOF. Offsets are 24-bit, so the practical ceiling is 16 MiB, the same cap as the constant in the IPS module. A record with length zero is run-length encoded. There is no checksum of the source, the target, or the patch. That is why a successful IPS apply can still boot to a colored screen. BPS, published by byuu as public domain, starts with BPS1 and ends with three CRC32 values: source, target, and the patch itself. Actions are SourceRead, TargetRead, SourceCopy, and TargetCopy. UPS starts with UPS1, stores both file lengths, then skip-and-XOR blocks. The XOR layout supports reverse application in a patcher that implements it; this site’s pinned UPS module validates the forward input only.
xdelta files are VCDIFF, the format in RFC 3284. Magic bytes on an xdelta3 stream are D6 C3 C4. xdelta3 can wrap windows in a secondary compressor. djw and lzma are the two ids this site's decoder accepts. Anything else stops with the secondary-decompressor message, which has its own page. PPF is the older disc-patch family. APS is two different files that share a nickname: APS10 on N64 and APS1 on GBA. RUP uses the NINJA2 magic. EBP is an IPS body with a JSON trailer, so its magic is still PATCH. BSDIFF and Paper Mario Star Rod modules apply here and do not build new patches.
I would pick BPS when the author publishes a checksum and the file is a SNES, N64, or GBA hack. I would pick UPS when the release notes name NUPS or say the patch is reversible. I would pick IPS only when the readme is explicit and the base is under 16 MiB. I would leave multi-hundred-megabyte DS translations and disc images on the xdelta page, and I would open Delta Patcher if the browser tab starts to swap. The four linked guides explain the most common format-specific workflows; the table also covers additional formats supported by the engine.