It's a messy situation, and overall I think LR has navigated the naming issue reasonably well (though not perfectly).
Photo apps have long used field names different from the industry-standard names, for a number of reasons: The old legacy standards were created for much different users and use cases (e.g. IPTC for the press), there are multiple standards with different names for what's essentially the same field, and product developers often didn't care about standards (e.g. very old Microsoft photo apps).
Consider LR's "Caption": It gets stored in three standard fields, EXIF:ImageDescription, XMP
escription, IPTC:Caption-Abstract. Yet most pro and consumer photographers have been trained by many apps and web services, not just LR, over many years to call it a "caption".
The various date-time fields are more confusing, no fault of LR. The EXIF standard (created by Japanese camera manufacturers) calls "capture date" EXIF
ateTimeOriginal. The EXIF
ateTime field (shown as Date Time in the Metadata panel) doesn't, as most users think, refer to when the shutter was pressed -- rather, it's when a camera or app conforming to the standard last modified the photo file. So I think it was reasonable for LR to call it "capture date" rather than by a name, Date Time Original, a name chosen by engineers for whom English was a second language.
Exiftool is very good about preserving the standards' field names, with some exceptions. By default, it shows the "pretty name" of a field (e.g. "Date Time Original"), but if you use the -s option, it shows the standard's name ("DateTimeOriginal"). There are some exceptions: It replaces "/" in IPTC fields with "-", and it rarely renames a field. For example, it renames the EXIF DateTime field to ModifyDate (perhaps because the author got tired of answering countless questions from confused users). And I recall it renames a very small number of fields that shared the same names but different meanings between standards (though I can't recall those offand).