A weak acid and a strong acid of the same concentration
will produce the same amount of product from the same
amount of reactant but the weak acid will take longer to do it.

The ionisation of a strong acid is complete.
A weak acid is only partly ionised.

The ionisation of a weak acid (for example ethanoic acid) is reversible.

ethanoic acid (in water)      hydrogen ion  +   ethanoic ion
CH₃CO₂H_(aq)                         H⁺_(aq)       +      CH₃CO₂^-_(aq)

The number of hydrogen ions produced by a weak acid is small.
When they have reacted with (for example) magnesium
more of the ethanoic acid molecules will ionise to produce
more hydrogen ions and ethanoic ions (see Le Chatelier's Principle).
Eventually all of the ethanoic acid molecules ionise and
react with magnesium and so the
same amount of product (hydrogen gas) will be produced.