The problem comes down to the usual KISS approach's leading to misunderstandings associated with well-intended simplification.
You don't appear to tell us much about your knowledge level so I am presuming you are a student pilot or thereabouts without an engineering or similar technical background ?
Lift coefficient depends on angle of attack, Mach Number (ie compressibility effects), and Reynolds Number (ie viscosity effects). The last two (M and Re) generally are ignored for most aircraft which operate at well below transonic speeds and in a narrow band of the atmosphere. Hence the low speed pilot rarely gets to talk about their effects - in any case they are conveniently hidden away in the CL data.
Many pilots have a basic understanding of Mach Number and, generally, none in respect of Reynolds Number.
Any number of net references, including these -
(a)
Mach Number
(b)
Reynolds Number
Most pilots tend to think of the simplistic CL versus alpha curve as being the whole story ... when it isn't.
The effect of M on CL is to reduce max CL as M increases. Some data relating to the DC9 is shown at Fig 11 in
this paper. A useful Boeing article on
angle of attack is worth a read as well - fig 4 shows some Mach effects.
The effect of Re on max CL can be seen at p60 in
Aerodynamics for Naval Aviators.