In the clinical laboratory, we are familiar with qualitative and quantitative methods. But what exactly are semi-quantitative methods?
Laboratories study properties of the samples delivered to them. In metrology, there is a scheme of scales designed to classify results based on the statistics which can meaningfully be applied to them. Four different scales have been identified : nominal, ordinal, difference (also called interval), and ratio. The ordinal, difference and ratio scales deal with properties which can be measured, and these apply to quantitative methods, which report quantitative results (usually concentrations). The difference scale is a rare bird; the only one in our field would be temperature. Its characteristics are identically sized quantity intervals and a randomly chosen zero. Most laboratory quantitative methods utilize the ratio scale. The name indicates that the units are equally sized, the ratio of the quantity values and amounts e.g. concentrations is constant, they have a natural zero, and results cannot be negative. This is the highest scale, and all statistics apply.
The least requirement for a "quantity" is that the results can be ordered according to size. This complies with the ordinal scale. Units of the ordinal scale can be of any size and need not be identical in the entire measuring interval, but they can be ranked (i.e. "small", "moderate", "large").
Results on the nominal scale describe properties which cannot be measured, they are examined. The results cannot be ordered or ranked; they are simply names e.g. cakes on a plate: chocolate or vanilla. A nominal property can include more than two alternatives, e.g. animals on High street: horses, goats, dogs. This scale applies to qualitative methods, which report a categorical result. In many cases it is simple to differ between results on nominal and ordinal scales. If you either have a piece of a cake on a plate or an empty plate, you are on the nominal scale. But once you start to "semi-quantitate" the meaning of "piece" (a nice slice or a few crumbs) then you have moved to an ordinal scale. Any procedure that gives results that can be ordered by size should be regarded as "quantitative". Calling it "semi-quantitative" seems to indicate that the result is not very accurate (true and precise) but still expressed on an ordinal scale. Also the specificity may be compromised, e.g. compared to results obtained by mass spectrometry (MS).
Does it matter? Yes, it does, not only because the term semi-quantitative has become lingua franca in our world. If a test examines a nominal property, only equality matters. But, by recognizing that the result depends on information (i.e. a signal) which has an inherent uncertainty, you communicate a quality of the result. The uncertainty of classification is specified by the probability that a certain indication occurs in a range centered on the target, or cut-off, value. The smaller the range, the better the test performs in terms of differing between the two possible outcomes; changing the target value will change the result. The cut-off cannot be changed on a nominal scale – a cake is a cake! Quality indicators that can be used for nominal properties, are difficult to generalize.
So, let's recognize semi-quantitative methods as those giving results on an ordinal scale with less-than-optimal quality indicators for trueness, precision and detectability or analytical specificity. They offer additional information compared to qualitative ones and communicate that all measurement have some degree of uncertainty.
 SS Stevens. On the Theory of Scales of Measurement. Science 1946; 103, (2684):677-680.