Let's look at the options available.
- WTO terms
- CETA ("Canada style" agreement)
- Single Market
The first one, WTO terms, is the minimum baseline agreement. As both the UK and the EU are WTO members, it applies automatically in the absence of any other agreement. It sets maximum tariff rates and dictates many other aspects of trade with regards to non-tariff barriers and trade in services.
A CETA type agreement would eliminate tariffs on most goods, set quotas on agricultural goods, expand provisions for trade in services, provide a means of smoothing over non-tariff barriers, and provides a dispute resolution mechanism. It's the non-tariff barriers which are the most significant, as WTO tariffs are in most cases already very low.
Under a CETA type agreement, neither side is obliged to change things like food standards or worker protections to any significant degree or to adopt common standards. What they do is provide a means for facilitating that exporters meet the standards required in the destination country.
For example, let's suppose a company wants to set up frozen pizza manufacturing in both the EU and in Canada. Let's call them say "Dr. Oetker's Frozen Pizza", to pick a real example. While manufacturing primarily for the local market, they also want to be able to offer specific recipes made in each factory in the other market. That way they can try out sales of recipes in each market to see how well they will sell in that market without having to set up trial production on both continents.
In order to sell German made pizzas in the Canadian market they have to meet Canadian food standards, and to sell Canadian made pizzas in the German market they have to meet EU standards. So to take the German made pizzas as an example, the production line and supply chains all have to get certified, all the way back to the farm in some cases, that they meet Canadian standards, upon which they get to put a Canadian food inspection agency stamp on their packaging and are allowed to sell in the Canadian market. They are also subject to inspection by Canada at any time.
Now apply this example to everything from food to electrical goods to furniture to machinery, etc.
This has long been possible in both directions without a trade treaty, as is obvious by all the cheap Chinese tat that is sold around the world. What CETA does is reduce the regulatory barriers to getting certified by defining all the hoops that must be jumped through and what reasons certification can be denied for. This is a large part of what is meant by reducing non-tariff barriers.
What the above is not is "Single Market". Single Market in EU speak is every member of the Single Market has incorporated EU regulations into their domestic law and regulatory systems. This means for example there is no need to certify individual pizza factories or their suppliers for export to the EU, as they already as a matter of course meet those EU standards. A pizza made in any part of the Single Market should, at least in theory, meet all food standards in any other part of the single market.
However, the assumption behind the Single Market is that all members have transposed the applicable EU directives into domestic law. And the arbiter of whether they have done so adequately is the EU court. So being a member of the Single Market inherently means adopting EU law and being subject to the jurisdiction of the EU Court.
However, being subject to EU law and the jurisdiction of the EU Court is what Johnson has said he doesn't want. Rather, he wants what's behind Door #2, which is CETA. This is where sovereignty comes into play as this is the test by which is it judged whether the UK has actually left the EU.
In practice, the UK may not choose to change their laws or regulations to diverge significantly from those of the EU in a manner which would affect say the manufacture of frozen pizza. They do not however want to place themselves under EU law or the EU court because that would severely limit them when making trade treaties with other countries as they would not be able to agree to standard trade treaty provisions such as regulatory equivalence or dispute resolution mechanism, as those would be the province of EU law and the EU court.
To put it more succinctly, Single Market is the EU camel's nose in the UK tent, and so that is why Johnson doesn't want it.