Hi Glenn,
A latex mattress needs just a solid base with enough supportive surface to make sure that it doesn’t sink through any gaps and that the base is strong enough and supported on the floor well enough to take the weight of the latex mattress and the people that sleep on it. Normally this means that a slatted wood or metal base (what you were calling a frame and I call a foundation) is the best. Both of these are rigid non flexing bases.
You can also use a more expensive tension adjustable slatted base like this, or this which typically uses thinner hardwood bowed slats and allows for the tension of the base in certain areas to be adjusted. This can fine tune the alignment on the mattress and “firm up” the support under the hips or allow the shoulders to sink down more. These work best with mattresses that are thin enough for the adjustments to be effective on the surface of the mattress.
You can also put the mattress directly on a slatted platform bed such as this as long as the slats are spaced close enough together and that the bed is supported in the middle so it doesn’t sag. Putting the mattress directly on a bed means that a base or foundation isn’t necessary.
There are also position adjustable bases like these which allow you to raise and lower the head and feet or turn on a vibrating massage and sometimes have all kinds of bells and whistles. These are also suitable for a latex or any “bendable” mattress as long as the weight limits of the motor are not exceeded.
Of course there are also combinations of slatted bases which are both tension adjustable and position adjustable like the legras here or the various Axel Bloom models. Ikea also makes a variety of different budget foundations including slatted bases and tension and position adjustable bases but there are mixed reviews about their durability and quality (NOTE: their adjustable foundations are no longer available).
So regardless of what you call it … a latex mattress needs a strong and evenly supportive base with strong slats that are no more than 3" apart (preferably closer to 2") or a metal base (that you and others were calling a frame) that has enough support surface area to prevent the latex from sinking through any gaps.
Most bases (what I call a foundation) come in various height options which allow the surface of the mattress to be at a certain height. They in turn can also go on a metal or wooden bedframe. Some have attachable legs of various heights to raise them off the floor. Regardless of all of this … the mattress needs to sit on a firm base which will not sag over time (more than it’s designed to) under the weight of the mattress and the people on it.
With wood foundations … the more wood that is used and the higher quality of the wood and construction that is used … the more expensive they are. For example a very high quality wood foundation with wool or cotton padding on top like this, … or this, … or these, … or this, is more expensive than some of the ones that you put together yourself and that use less wood or thinner wood.
Some wire grid metal platform bedframes can also work well as the metal is very strong and as long as the surface area is enough and the wires are close enough together to ensure that the mattress doesn’t sag through or damage the latex … then they would probably also be fine although they may be a little more risky for an all latex mattress in the longer term (see post #10 here). There is a variety of different designs and some use more or less steel of different gauges so here too quality usually determines price. In many cases, steel foundations made by leggett and platt or hickory springs are placed on wooden bases and then the quality of the bases that the metal assembly is attached to is also important. Versions like the Zinus metal foundation (or the many variations that are similar) are also a less expensive option that seem to work well even though the wires are thinner.
All in all there are too many base options for me to keep track of so I prefer to help people with ideas about what to look for and in most cases I would just follow the recommendations of the manufacturer who is selling the mattress as they will know which bases work best with their mattresses.
Many local outlets will sell you a foundation (just make sure it is suitable) and a few phone calls to find out at local manufacturers or mattress outlets in your area may well be worth while as long as you can verify that the foundation is suitable for your mattress. If they don’t and the outlet where you are buying your mattress doesn’t have foundations that you believe are a reasonable cost … then an online purchase makes sense to me.
Hopefully this will help sort out the foundation, base, frame, bed, platform, options for foam mattresses 
Phoenix