Cell-level selection and inheritance of acquired mutations
In any reproductive event, we transmit new mutations to the offspring. In absence of cell-line selection, whether the mutation occurred during a meiosis or a mitosis is of little interest.

In absence of cell-line selection

A big difference between acquired mutations and Lamarck's acquired inheritance is that under Lamarck's view point, characters are being adaptive. Under Lamarck's view point, individual try to perform some action, stretch their muscles and other organs toward what is optimal for their needs and this phenotypic modification is being transmitted. The classical example is the example of giraffes. Giraffes stretch their neck trying to reach for high leaves, their neck is getting longer and their longer neck is being transmitted to their babies.

With acquired mutations, in absence of cell-line selection, there is no reason for adaptive mutations to be transmitted more often than non-adaptive one.

With cell-line selection

Now, if there is cell-line selection, beneficial mutations (beneficial at the cell level) are more often transmitted. The mutational process itself stil remain "random" (see Are mutations random?) but selection will increase the ratio of beneficial to deleterious mutations. Now, mutations that are beneficial at the cell level are not necessarily beneficial at the organism level. A typical example is cancer.