Is any text which reports variant readings from other manuscripts a “critical edition”? And what is a diplomatic edition?

A text which reports all variant readings from various manuscripts without selecting a preferred one is a collation. In a collation, one typically reproduces also variant readings which are clearly wrong and will later be eliminated. Some of these details are irrelevant for the sake of the constitution of the critical text, but can be relevant for the history of the transmission. For instance, a manuscript often writing śa or ṣa instead of sa might be an evidence of the fact that the text was transmitted (at a certain point of its history) within an environment in which the dental sibilant was not distinguished, e.g., in Bengal. The same could be repeated, mutatis mutandis, about the use of retroflex ḷ for non Vedic words, the confusion between sounded and unsounded occlusives and so on.

If you have a single manuscript, or a manuscript which has an important history (e.g., it was composed or used by an important scholar), you might consider producing a diplomatic edition of it, i.e., an edition which reproduces as much as possible all the peculiarities of the manuscript, with as less editorial interventions as possible. You will try in this case to be as close as possible to the manuscript, reproducing all that may be relevant, e.g., ornaments, marginal corrections, string-holes, line breaks, avagrahas, halants and the like. Much of this information could be considered to be irrelevant, so that it will not be included in the critical edition, but it may be of relevance if you are trying to reconstruct the way the copyist thought of the text he was copying (or composing!). More on this below.

A critical edition has to be, first of all, critical. Variants like karanam instead of karaṇam are needed in the collation and in the diplomatic edition, but have usually no space in a critical edition. Don’t fill your apparatus with meaningless variants which have the only purpose to show that you read many manuscripts:-) Read them and record them in the collation, then start working at your critical edition.
Now, there might be border-line cases. For instance, let us consider the case of a reliable and of an unreliable manuscript. The latter is typically a manuscript which is usually full of automatic mistakes, e.g., dropping syllables or missing a line if it starts with the same word as the previous one, and where one has the clear impression that the copyist and its successive readers were not understanding what they wrote.
By contrast, a generally reliable manuscript is one where variant readings tend to make sense, so that one is sure that its copyist (or its successive readers) was accurately going through the text they read.
Now, let us admit that the former manuscript has a variant which happens to make sense, e.g. bhāti instead of the expected bhāvayati. I am inclined to think that one should not put it in their critical apparatus and rather just explain in the manuscript’s description that it tends to drop syllables. However, if one were to find the same type of variant in the generally reliable manuscript, I would highly recommend keeping it in the apparatus.

At this point, one might ask why keeping variants such as karanam for karaṇam in the collation or in the diplomatic edition. Within the collation, as hinted at above, they are meant to be useful in order to reconstruct the history of the transmission. In the diplomatic edition, I would be even more precise in reproducing the writing peculiarities of the single and precious manuscript one is focusing on, because every element could be useful to reconstruct its copyist’s way of thinking.
For instance, suppose one encounters the reading शब्दोनित्यः in a Nyāya manuscript. This can be easily read as meaning in fact शब्दोऽनित्यः, since avagrahas are often missing in manuscripts and the scriptio continua is the norm. Hence, it is essential to note when and whether at all avagrahas are employed by the copyist.
As a different example, let us take the reading अग्निहोत्रमधर्मः in a Mīmāṃsā manuscript. In my experience, copyists might forget halants, so that this can be interpreted as agnihotram dharmaḥ (i.e. agnihotraṃ dharmaḥ). Thus, it is fundamental that the editor distinguishes these two cases: अग्निहोत्रम् अधर्मः and अग्निहोत्रमधर्मः. Both could be transcribed as agnihotram adharmaḥ, but I hope that it is clear that the former is way more likely than the latter to really mean agnihotram adharmaḥ. Thus, let us transcribe, in a diplomatic edition, the former as agnihotram± adharmaḥ, using “±” or any other symbol to indicate the halant. Similarly, I would suggest using a symbol for the string-hole (I use “§”) and for each line break (I use “//”), since these are points at which a copyist is likely to make small mistakes, e.g., forgetting a halant or a vowel sign, or even missing a line. Indicating the string-hole or the line break helps the editor (and their successive readers) evaluating the weight of each evidence.

Long story short: Be clear about your goal. Are you reproducing an important text as you found it in a single manuscript? Do a diplomatic edition and, only thereafter, a critical one. Don’t mix the two by reproducing the text and yet adding your conjectures. Keep your conjectures for the next step, the critical edition, where you will be able to emend the text also on the basis of parallel readings found in similar texts, quotation of the text in later texts or quotations in the text of earlier ones (see Steinkellner 1988 (and Freschi 2015) for a discussion of all these cases).
Are you collating many manuscripts in order to reconstruct the history of the transmission of the text? Be as precise as possible. Are you trying to reconstruct the text as it was composed in, say, the 16th c.? Do a critical edition and avoid wasting your readers’ time and energies with variant readings which have only a phonetic or historical significance. Focus instead on real variants, especially if they represent really alternative texts. For all the rest, write a description of the manuscripts you used, explaining their peculiarities (e.g., always writing a single -t- before a consonant, as in satva).

I wrote the above thinking most of all of my students and younger colleagues. If you are among them, is there something else you would like to know?. If you are an experienced colleague, do you agree? What would you change?