The answer is "yes", "no", and "maybe". if it is not a synthisised multi-mode set it will probably be continuously tunable although the part of the band that was being used is by gentleman's agreement FM only, and the convention is to use specific frequencies (which relate to channels). A synthisised set can be programmed for different channel steps (spacing) and will appear to step from channel to channel - if these steps are made very small, it will appear to be continuously tuned. They usually display the frequency in use, but some can be programmed by the user to show any chosen text, so that could be a channel number.
On Sunday the quick comments were about channel 21, which is used on Sunday morning at 11:00am for a news broadcast, so we picked 22 instead. These numbers are actually out of date now. The standard spacing for amateur service was formerly 25kHz but it is now 12.5kHz. To accommodate the change all the channels on most of the bands were renumbered. However, as the centre frequency of the "channel" is what is being refered to by the channel number, that has not changed whether we call it S22 or XYZ916. So we were working on 145.550MHz.
It is all very confusing until you do the RSGB exam course where much will be explained.
73s