I have learned that the notation to classify spiral galaxies in the De Vaucouleurs system goes like "SA for spirals without bar, SB for spirals with bar and SAB for intermediate spirals". But in some places I've seen galaxies classified as Sa or Sab for example. What it means and what is the difference between a Sa and a Sab spiral?
Capitalization is critical here. (As is knowing which classification system is being used.) The traditional spiral stages (going back to Hubble) are Sa - Sb - Sc; this was a sequence from more centrally concentrated (more dominant central "bulge") + smoother disk + more tightly wrapped spiral arms (Sa) to less centrally concentrated (smaller or even nonexistent bulge) + less smooth disk + more open spiral arms (Sc). Later, S0 (for lenticular galaxies, which are not spirals but seem to have significant or dominant disks) was added at the beginning and Sd (and sometimes Sm) were added as stages beyond Sc.
Hubble also specified that clearly/strongly barred galaxies should be labeled SB0 - SBa - SBb - SBc (with a later extension to SBd), creating a parallel sequence to the nominally unbarred sequence S0 - Sa - Sb - Sc - Sd.
De Vaucouleurs emphasized the existence of intermediate stages: thus, Sab is in between Sa and Sb, Scd is in between Sc and Sd, and so on. (There is also a stage intermediate between S0/lenticular galaxies, which are not spirals, and the Sa spirals: "S0/a".) He also applied this to bar classifications, arguing that there were weakly barred galaxies in between unbarred and strongly barred galaxies. To do so, he changed the Hubble classifications so that "SA" mean unbarred, "SAB" mean weakly barred", and "SB" meant strongly barred. These precede the lower-case Hubble-sequence labels, so you end up with SA0, SAB0, SB0 - SA0/a, SAB0/a, SB0/A - SAa, SABa, SBa - SAab, SABab, etc.
To add to the confusion, de Vaucouleurs also recognized that some spiral galaxies had an unclear bar status (especially true for edge-on galaxies). His famous and widely used RC3 catalog uses "S" for those cases, so "Sa" in RC3 actually means "Hubble stage a, unknown bar status". This, of course, looks exactly like the traditional Hubble classification (continued by other classifiers such as Allan Sandage) meaning "Hubble stage a, unbarred), which has confused people over the years.
To directly address your question: the "a" and "ab" mean what you said in your comment: "Sa galaxies tend to have significant bulges, and tightly-wrapped and relatively smooth spiral arms. Sab galaxies are similar to Sa galaxies, but show more obvious resolution of the arms." Loosely, people will often use "Sa", etc., to refer to spirals regardless of their bar status, as in your quoted text (or in something like, e.g., "Sa galaxies tend to have lower star-formation rates than Sc galaxies."). If it's a specific classification of an individual galaxy, then it might mean "also unbarred" or even "bar status unclear".