The PCR test measures tiny amounts of virus. LFTs measure whether there’s detectable replicating virus, i.e. whether you’re likely to have enough virus in your nose/throat to be infectious.
There’s no direct relationship between how much virus you have in your body, and symptoms. I have an overactive innate immune system and routinely get flu-like symptoms with diseases I don’t catch. For example, both my little boys got chicken pox in September and I spiked a 38.5 degree C fever the day before they came out in spots, and then had itching/joint pain/fever until the spots crusted over.
I haven’t bothered doing a PCR as we’re all self-isolating, but my DH tested positive on Xmas Day by LFT/PCR - having begun symptoms on Xmas Eve. Since the afternoon of Xmas Eve, I’ve had (variously) a sinus headache, violent sneezing, a fever over 38 degrees C, dry eyes, blocked tear ducts, multiple mouth ulcers, tickly throat, a ‘scorched’ feeling in my windpipe, chest pain, a dry cough, dry mouth, bouts of itching on my arms/waist/ankles, stiff wrists/toes, and nausea. The symptoms get worse if I’m in a poorly-ventilated room with my DH for more than an hour, and get better if I’m stood outside in the open air.
At no point have I tested positive on a LFT - and I’ve been taking them daily as a close contact of a household case. Thus, all those symptoms were caused by my innate immune system reacting to airborne virus - rather like allergies - and not to my viral load.
Hope that clarifies… And, yeah, it is weird.