Is there any difference between strain and mutation/mutant?

You can think of "strain" roughly analogous to how you would think of "breed" in the context of dogs or horses.

There might be some key mutation that identifies members of a strain over non-members, but you would expect to find other genetic differences as well. "Strain" for a virus is not referring to a particular mutation but to the viruses on one side of some fork in their evolutionary history.

As @BryanKrause has correctly pointed out, strains for viruses and bacteria are the same as breeds/races for mammals and birds - the differences between strains are sufficiently small that they cannot be considered different species, yet they may differ by more than one mutation.

Strain is a somewhat generic term, whereas more refined terminology may exist for every particular virus. For example, in case of HIV one distinguishes types of virus (HIV-1, HIV-2, SIV), the groups within each type, and the subgroups. Depending on the context any level of this taxonomic division can be referred to as "strain".

What further makes distinguishing strains difficult is that breeds/races are usually defined by having different phenotypes. The phenotypical differences between different viral strains are more difficult to define, so it is not uncommon to distinguish different strains (or even species, as in the case of flaviviruses) simply by the number of mutations or the fraction of nucleotide differences between sequences.