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The fundamental String of IIA String theory is the M2 brane of M-theory wrapped on the M-theory circle at weak coupling limit. The weak coupling limit is when the radius of the compactified circle is very small. More generally at weak coupling limit the best description is the IIA string theory while at strong coupling limit the M-theory description.

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There are no fundamental strings in M-theory. M2 branes can end on M5 branes and these appear as strings in the world volume of the M5 branes but these strings are of solitonic nature.

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M2 and M5 branes are fundamental objects of M-theory. You can see this from the superalgebra of $D=11$ SUGRA, which is the low energy limit of M-theory. Moreover M2 and M5 couple respectively electrically and magnetically to the RR 3-form $A_3$ of $D=11$ SUGRA. In the compactification limit for the eleventh dimension, from M-theory you get the $IIA$ ...

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