Yes it doesn't refer to income, but rather to the way in which people generate that income and the property relation concerning that. The proletariat does it through labor, the bourgeoisie through ownership of the means of production and letting other people work for them. That being said, if you'd look at these groups ones you've drawn the line though, you would still likely have had found similar results of economic outcome and social status.
However the actual poor, unemployed, unsteady employed, working poor, individual service workers and others who struggle to stay alive, he would have grouped outside of the two classes as "Lumpenproletariat" who he categorized as unreliable and lacking the class consciousness of the proletariat and which are thus detrimental to the workers revolution.
Also one thing to keep in mind is that when Marx was around the economy consisted largely of the primary (agriculture and raw material) and the secondary (industries and manufacturing products) economic sector. Making a shift from the primary towards the secondary sector. That is, he saw and predicted that the individual manufacturers and small producers of raw material will be pushed out of business by the industrial producers who can do it faster (due to machines), cheaper (due to a decreased amount of labor) and more reliable (due to machines). And so production of goods will move from unique and individual to collective and standardized. So you had this alienation from labor, previously people made a whole product from start to finish now they only produce one part of it and the product quite literally doesn't bear the name of the creator anymore, but the name of the company owner (brand).
And so he saw this productive wage labor (in the sense that they produce something), as the new dominating form of labor. The freelance producer was on it's way out and the service industry was likely not significant yet, so the focus was on the industrial worker.
And for that group owning the means of production or not, was quite significant. They could operate the means of production and produce the necessities of their society by themselves, in fact they already did that, but their socio-economic and political status was still that of an underclass. While the production is collective, the distribution of power, agency, capital, work and rewards in that collective is massively unequal.
So it's not entirely unreasonable to ask the question whether white collar workers were even fully included in that classification or whether they were just treated as an edge case. Like sure you could abstract the classification and speak about "petty bourgeoisie" and "worker aristocracy" as bourgeoisie and proletariat, but at some point this becomes quite questionable.
I mean the petit bourgeoisie was never meant to last or be significant according to Marx, who apparently firmly believed in the potential of the industrial revolution to wipe out all small producers. So either the petit bourgeoisie would become regular bourgeoisie or drop down to proletariat or lumpenproletariat. So they held out a lot longer than they were supposed to. Not to mention that the industrialized production and the standardization wasn't all as great as anticipated. Sometimes you need unique and specialized production and the more optimized the process is, the harder it is to "just change it". So a lot more companies survived in a niche than what was anticipated by Marx.
Likewise the "service sector" was probably largely insignificant at the time and is now the single largest and most heterogeneous economic sector. Which ranges from "Lumpenproletariat" to industrial wage workers who are not hired directly but just "on demand", to clerks, mind workers all the way up to the management and CEOs. Which span a huge group of people who are hardly in similar economic, social and political relations. So it takes a lot of mental gymnastics to argue that CEOs and upper management are in the same class as the person cleaning the toilets. Despite being wage workers rather than capital owners they themselves are responsible for hiring and firing people and take a share of the bounty of the exploitation of people below them in the food chain and if they wanted they could even use their capital to become an owner.
Or just in general how for many of these people the "means of production" become a lot more nebulous. Like for explicit service jobs and not masked "non-contract" employments the source of income is the existence of rich people who can afford that service. So preserving a well of upper class who spends money lavishly is what keeps many people in business. So if workers took over the means of production they'd be screwed. They are technically lumpenproletariat.
So the more people are pushed away from the primary and secondary sectors the more they are further alienated from labor and the source of their existence. In Western countries these things might even be totally moved to other countries. Like there are thriving countries who are purely service no agriculture not production at all.
So on the one hand it's the single largest sector, makes up the new mode of labor. On the other hand the description of proletariat doesn't really fit.
Though you could still argue that the abstraction sorta kinda could be applied as people in employment still have a different perspective in terms of agency over their own work, which would differentiate the truly petit bourgeoisie from the "pseudo-self-employed" you know your uber driver or freelancer who basically works as an employee for just one company but because that employer wants to avoid social security and other benefits related to a contract they just hire them ondemand as a "self-employed entrepreneur" when in reality it's just a shady scheme to avoid paying people.
So you can argue that the owner/worker distinction still kinda sorta implies, but it's questionable as to whether you're still talking about the same thing that Marx referred to or whether we are already progressed further and thus are talking about different categories. I mean he himself argue that previous societies also had class relations. So just because you can make out a class relation doesn't mean you're talking about the same economic conditions.