If someone tests positive are they contagious for 2 full weeks or just until symptoms are gone?

We've had a spike around where I am at. One lady was exposed and tested negative, twice, but the health department told her she had to stay quarantined for 2 weeks. Is this because she still could develop covid? 

Another gal who tested positive was told as soon as her symptoms were gone she could come out of quarantine.

I believe they worked together but I'm not positive. 

It kind of feels like this is a make the rules up as you go deal

I'll try to clear up a few things here.  First, we are learning things about this new, "novel" virus almost on a daily basis.  Some of the changes and reversals in the recommendations have come about as a result.  For example, antibody testing suggests that over 5% of the entire population has been exposed to Covid19. We may learn that number is closer to 10%, eventually.  That means that 15-30 million Americans have been exposed, and we know that from antibody testing.  Actual nasal swab testing for the Covid19 virus antigen is generally done on people with a history of close contact or people with symptoms.  Random testing for Covid19 antibody, on the other hand, suggest this is much more widespread. We don't know how long these people will have detectable antibody, but if it remains for a long time, we could really develop meaningful "herd immunity".  There are two coronavirus subtypes that cause the common cold.  In those cases, meaningful memory typically only lasts about 2 months.  Then, as some of us have experienced, bang....we get another cold.  Our hope is that Covid19 stimulates the formation of "T memory cells" and "B memory cells" which can be dormant....until the antigen is contracted again, at which time these cells rapidly differentiate into antibody secreting clones of B cells that produce antibody at a much more rapid rate and quantity.  That secondary response is typically much more intense, in terms of antibody production.....in other words, it is amplified.  Right now, we don't know the duration of immunity.  Viruses like varicella (chicken pox) impart life long immunity, or at least very long immunity....decades. Other viruses like influenza or cold viruses, such as the corona viruses I mentioned, only confer immunity that lasts a couple months or maybe a year.  I can't explain that.  

Here's another new finding.  Three months ago we were told Covid19 can be detected on hard surfaces for up to 8-9 days.  The latest is that the transmission of Covid 19 from hard surfaces has been overblown, and now the official word is that this fear has been vastly overblown.  

Here's another new finding.  Asymptomatic Covid19 patients are not nearly as contagious as was once thought.  That too has been overblown, according to none other than the WHO.  WHO however has serious credibility issues, as we all know.  Some countries have done extensive "contact tracing" of asymptomatic Covid19 positive people and they have concluded that transmission from asymptomatic Covid19 patients is "very rare".  My opinion?  Play it safe.  If you test positive and remain asymptomatic, I would recommend you stay away from grandma for at least 2 weeks, and get re-tested negative before exposing others....especially those at risk for sever disease and death.  Data keeps emerging, so until there is solid consensus, play it safe.  

Now to answer your questions, specifically.  If someone tests positive, and remains asymptomatic, like I said above, I'd play it safe, as much as practical. If someone has symptoms, I would rely on a negative Covid19 test (swab) but wait for 2 weeks after symptoms have resolved.  Keep in mind, this illness can last as long as 6 weeks, especially in people who become very ill.  

As to the lady who was exposed but tested negative twice, keep in mind, no test is 100% sensitive.  You can get false negative testing, although it isn't very common.  If she tests negative twice, and an antibody test is done, if she is positive for IgM but negative for IgG, then she has recently acquired Covid19, probably within 5-10 days. In that case, yes, she should probably remain quarantined for 2 weeks.  If she is symptom-free and is positive for IgG only, then she can go about her normal daily business.  She is probably immune and viral shedding in those people is very very rare. 

In the last case you asked about, she should be tested for Covid19 after her symptoms subside and can come out of quarantine if she tests negative.  Alternatively, if she has serologic testing and tests positive for IgG, then she has immunity and viral transmission from those people is almost nil.  

Just to review, in case there is confusion, the typical response to a virus or bacteria is first with IgM.  That's a molecule 5 times as large as IgG.  It appears between 5-10 days, and rapidly wanes.  Basically it holds down the fort until the much longer-lasting IgG comes on the scene and takes over the battle....that appears by about day 14, and sticks around for a variable period of time.  Development of those memory cells is the key to long term immunity.  It's all about the clones.

I'd better stop now.  Forgive my lengthy answer.  I love this stuff.