mutations, variants and strains
The use of the term mutant in biology is neutral. It just means that there has been a change in the genome of a living thing. Such mutations occur commonly, especially in viruses, and, for the most part, are harmless in that they are unsuccessful. It is as if you took a sentence and randomly changed a letter here and there. The sentence remains meaningful but the odd letters are meaningless static. But you can by sheer luck get a set of changes to the letters that produces a new sentence with a new meaning. The DNA in a virus is changing all the time in that way and usually without affecting the nature of the virus, but every now and then a virus will produce a mutated form that changes the behaviour of the virus. This is given the name variant.
The difference between a variant and a strain of a virus is really a question of degree. A variant has a few genetic changes but is still essentially the original virus. A strain is changed to such a degree that it can be regarded as a separate virus. Strains can occur naturally or be developed in a laboratory.
The fact that we are probably more familiar with the sci-fi mutant than the biological mutant means that we regard virus mutants as intrinsically scary, but the vast number of them are irrelevant. The occasional ones that work could go either way, that is, make the virus more or less powerful. The British and South African variants have become more infectious but are still vulnerable to the vaccine. There is now a Brazil variant, which was identified in early January this year. It has a number of additional mutations and it remains to be seen if it can still be recognised by antibodies.