Does Thermoplasma have cell wall?

I did not understand the part where it says: "the presence of the cell wall does not rule out that Thermoplasma may have other types of wall or membrane.

Is there any research on the structure of the wall of Thermoplasma? And how do you differentiate a true microbe from a "wierd thing" that does not grow or is not a true bacterium? I know of the genus 'Streptococcus' which is commonly found in the human throat. It has many sub-species which could be defined as bacteria but what exactly makes this group different from Pseudomonas aeruginosa? The problem with those taxonomy systems is that they are designed for animals and are based on an evolutionary concept. If were to use them for microbes, many (if not most) bacteria would have to be reclassified. Also, they are just guidelines; the fact that an organism falls into one group does not mean that it should be placed in the group's parent class. But most importantly, there is no universally accepted system that is not arbitrary and can be used on all microbes.

So what exactly is a non-bacterium? Are there more species of a genus (say Escherichia coli) than there are genera? I read somewhere that "all bacteria have flagella but not all bacteria are motile". What is the difference between a bacterium and a non-bacterium? The Wikipedia article says: "Non-motile, Gram-negative bacteria have an outer membrane that prevents passage of material between the cytoplasm and the environment. Non-motile Gram-positive bacteria do not have an outer membrane, but are able to move by a process called twitching, ie the movement of protoplasmic bands that contract on the surface of the cell."

This is confusing to me. How do you tell whether a bacterium is motile or non-motile? I've never heard of anyone motility testing. Please give an example of how to distinguish between a bacterium and a non-bacterium.