What is the difference between meristem and bud?
I looked in Taiz and Zeiger. Plant Physiology 5th ed and this is what I found:

Plant growth is concentrated in localized regions of cell division called
meristems. Nearly all nuclear divisions (mitosis) and cell divisions
(cytokinesis) occur in these meristematic regions. In a young plant, the
most active meristems are called apical meristems; they are located at the
tips of the stem and the root (see Figure 1.1). At the nodes, axillary buds
contain the apical meristems for branch shoots.
The root and shoot apical meristems formed during embryogenesis are called
primary meristems. After germination, the activity of these primary
meristems generates the primary tissues and organs that constitute the
primary plant body.
Most plants also develop a variety of secondary meristems during
postembryonic development. Secondary meristems can have a structure similar
to that of primary meristems, but some secondary meristems have a quite
different structure. These include axillary meristems, inflorescence
meristems, floral meristems, intercalary meristems, and lateral meristems.
Axillary buds are secondary meristems; if they are also vegetative meristems, they will have a structure and developmental potential similar to that of the apical meristem.

So, briefly, I could say that meristems are localized regions where undifferentiated cells reproduce themselves and originate new plant tissue. Axillary buds contain secondary (formed after embryogenesis) meristems. This meristem can behave like an apical meristem if it becomes vegetative i.e. either apical dominance disappears or it is excised and subcultured elsewhere.