The first one is a Dracaena deremensis, 'Janet Craig.' It does very well under fluorescent office lighting with no sun. Yours appears to be healthy although its appearance would benefit if the taller stem were pruned back and inserted in the base of the plant. Allow the top inch of soil to dry before adding enough water so that the top inch is dry again in a week. That won't be very much water.
The other plant is a Croton. It has been put into a pot that is much bigger than necessary and that increases the possibility of overwatering. Water it in the same manner that I described for the D. Janet Craig. Crotons do much better if kept close to a sunny window