An astonishing amount of people in Britain seem to think that EFTA and the EEA are the same thing, including some who really ought to know better (or at least have access to staff and resources to inform themselves properly).

The EEA = the European Economic Area, which stretches from Iceland to the Russian border.
It is better known as the Single Market or Common Market.

To be a part of it you have to be either in the EU or a member of EFTA.
https://en.m.wikipedia.org/wiki/European_Economic_Area

EFTA is the European Free Trade Agreement. It's a club of European countries that are not in the EU.

The UK was a founding member of EFTA in 1960, but alongside Denmark, it left to join the EEC in 1972.
https://www.efta.int/About-EFTA/EFTA-through-years-747

EFTA has 4 members at present, of which 3 are also in the EEA (Iceland , Norway and Liechtenstein ).

Switzerland is not in the EEA, but is a signatory to the EEA agreement and it has bilateral agreements that place some sectors of its economy in the Single Market.

When the UK left the EU, it also left the EEA so it's no longer a member of any of these.
It now has a new agreement with the EU (the TCA) and is in the process of negotiating a new FTA with the EFTA countries and bilateral agreements with Switzerland.

Some people say that the UK should have stayed in the EEA (Single Market) when it left the EU.

However, to be in the EEA is only possible if you are in the EU or EFTA, and as you can't be in both, a seamless transition was really not possible. https://twitter.com/patricklohlein/status/1355896648799571971?s=19

Of course, the UK could have applied to join EFTA during the transition in 2020 and from there applied to rejoin the EEA, but it didn't.
There is not much point in speculating why, but there wasn't much interest. The debate was "Deal or No Deal" - like a rubbish 1980s TV quiz.

(Much earlier, other alternatives, such as the "Noway+" model and "Continental Partnership" were tabled, which would have required changing the EEA agreement to create a separate pillar so the UK could be a member without being in the EU or EFTA, but these were abandoned)

Now there is much renewed interest in the @EFTA4UK option, we should be clear about what this means.

If the EFTA countries were to let the UK in, it would not mean that the UK is back in the Single Market. It would just mean the UK is in EFTA.

To rejoin the EEA as well, the UK would need to apply separately and get consent from all 30 EEA members (EU27 states and the EFTA3).

Being just in EFTA would make the UK much like Switzerland - with the important differences that:
a) unlike Switzerland it would have a framework agreement with the EU, but b) it wouldn't have all the bilateral agreements that the Swiss have.

We have to be honest that EFTA membership itself would have little effect on the new arrangements between the UK and EU, but it would send the EU a clear signal that the UK is firmly in the club of EU-sceptic countries and it could be a stepping stone towards rejoining the EEA.

Since we have studied the TCA, we also believe that it reopens the possibility of creating a third "independent British pillar of the Common Market", i.e. that the EEA agreement could amended to allow the UK to rejoin the EEA without being a member of the EU or EFTA.

The concept of an "independent British pillar of the Common Market" is quite new to the debate and while there isn't much appetite for it yet, we believe it will grow as the inadequacies of the TCA become more apparent, particularly in regard to Northern Ireland.

The EU and EFTA aren't the only groupings in Europe. There's also CEFTA - the Central European Free Trade Agreement @CEFTA_, which covers Albania , Bosnia and , Moldova , Montenegro , North Macedonia , Serbia and the UN Mission in Kosovo.
See https://cefta.int 

Lots of comments and questions on this thread asking about how long these options would take. The short answer is that it depends on politics, i.e. how soon the UK and EU are able to return to more amicable relations.

"Like it or not, the two sides are condemned to work together" explains @anandMenon1 with a longer answer and the assessment that "there are good reasons to think that tension between the UK and the EU is not a passing phase, but the new normal" https://theguardian.com/commentisfree/2021/feb/02/vaccine-rows-spats-eu-uk-competitor