Precursor miRNA and a mature miRNA
precursor miRNA is ~70mer RNA with a stem loop structure. It is cleaved by dicer to generate one or two mature miRNAs (from one or both the 'arms' of the stem ; called 3p and 5p which are ~22nt long). Refer to this review. (It is an old one and some facts might have changed, but the basics are there.)

Yes, there can be different precursors giving rise to same mature form. There are a few cases like that (check for entries like mir-x-y [where y can be 1,2,3,...], in miRbase). 

Usually pre-miRNA is shortlived and is immediately converted to mature form. Therefore, in small RNAseq data, most miRNA reads (more than 90% [at least that's what I get]) come from mature form (pre reads would be longer [after adapter removal] and will contain sequences not retained in mature form). Most algorithms select for the mature reads. 

It is difficult to determine which precursor gave rise to a certain mature miRNA, using an RNAseq data. The usual practice is to assign the average read count to each locus. E.g., for a mature form that has 3 precursors, each precursor is assigned 1/3 of the total mature reads. However, in most RNAseq experiments, the objective is to obtain the mature miRNA profile and which precursor gives rise to it becomes immaterial.