In terms of muscle: are the terms 'satellite cell' and 'muscle stem cell' interchangeable? That is, are there muscle stem cells that are not satellite cells, or vice versa?
Well, there is some level of ambiguity here. The distinction at terminology level between "muscle satellite cells" and "muscle stem cells" is generally made by those researchers who insist/emphasize that muscle satellites are not a homogeneous population, e.g. Kuang et al., 2007
we conclude that satellite cells are a heterogeneous population composed of stem cells and committed progenitors.
Or from a review summarizing that paper:
Due to their position on the surface of the muscle fiber beneath the basement membrane and their characteristic expression of the marker Pax7, satellite cells can easily be analyzed by standard immunofluorescence technologies. [...]
Recent studies have provided more evidence that satellite cells are actually a heterogeneous population where all cells express Pax7 but only a fraction also expresses the myogenic transcription factor Myf5 (Kuang et al., 2007). In vitro lineage analysis shows that the Myf5-positive satellite cells arise from the Myf5-negative cells. Upon transplantation, only the Myf5-negative cells contribute significantly to the satellite cell compartment whereas the Myf5+ cells preferentially undergo terminal differentiation. Thus, the Pax7+ Myf5- cells are true stem cells whereas the Pax7+ Myf5+ cells are more committed progenitors.
However, one has to keep some perspective that these "committed progenitors" are just the offspring of stem cells following a fairly usual asymmetric division strategy broadly used by stem cells in other contexts
Stem cells self-renew but also give rise to daughter cells that are committed to lineage-specific differentiation. To achieve this remarkable task, they can undergo an intrinsically asymmetric cell division whereby they segregate cell fate determinants into only one of the two daughter cells.
Muscle stem cells live in a niche, and the niche mechanism of asymmetric division appears proximity/orientation based, as Kuang et al. found:
Planar divisions were observed to give rise almost exclusively (92%, n = 89 pairs) to identical daughter cells that were either both Pax7+/Myf5- or both Pax7+/Myf5+ [...]
Strikingly, we observed apical-basal oriented doublets where the sister cells assumed asymmetric cell fates (82%, n = 38 pairs). The majority of apical-basal oriented doublets contained a Pax7+/Myf5- cell against the basal surface and a Pax7+/Myf5+ cell located on the apical side against the muscle fiber [...]. In addition, we observed rare events where the basal cell expressed Pax7 and Myf5 and the apical cell had downregulated Pax7 and was presumably undergoing terminal differentiation.
Again, this is a fairly common process, observed elsewhere/before, per the review:
the stem cell is in close contact with the stem cell niche and depends on this contact for maintaining the potential to self-renew (Li and Xie, 2005). By orienting its mitotic spindle perpendicularly to the niche surface, it ensures that only one daughter cell can maintain contact with the stem cell niche and retain the ability to self-renew. In contrast to intrinsically asymmetric cell divisions, which usually follow a predefined developmental program, niche-controlled stem cell divisions offer a high degree of flexibility. Occasionally, the stem cell can divide parallel to the niche, thereby generating two stem cells to increase stem cell number or to compensate for occasional stem cell loss. For this reason, niche mechanisms are more common in adult stem cells, whereas intrinsically asymmetric divisions predominate during development.
However, in contexts when one isn't so interested in the sub-populations of satellite cells during their division process, just their overall contribution to muscle repairs, the terms "muscle satellite cells" and "muscle stem cells" are used (more) interchangeably, e.g. Snijders et al. (2015) write in their review:
Adaptation in the context of skeletal muscle is often discussed as a change in structure and function in response to an exercise stimulus. [...] Skeletal muscle stem cells, also known as satellite cells, are now thought to play a significant role in the adaptive process.
Interestingly perhaps (from terminology standpoint), Nguyen et al. (2019) avoid using "satellite cell" altogether in their review and talk just of "muscle stem cells" vs "committed myogenic precursor".
To maintain this population, MuSCs may undergo symmetric or asymmetric division, respectively, producing either two identical daughter cells or both a single undifferentiated daughter cell and a committed myogenic precursor.
However this last approach kinda obscures (at terminology level) the anatomical location aspect/angle that gave rise to "satellite muscle cell" in the first place (see Snijders for a mini-history.)
Based on this review, satellite cells can replenish injured muscles, but among satellite cells there are satellite stem cells to maintain the pool of satellite cells.