They probably call it that because there are few social welfare programs and the government doesn't spend much. Third world countries are like that, so when a developed country does the same thing, it gets called third world, too.
If you think that any country is rich because of generous welfare system - G-d bless your naivete.
The truth, as ever, lies between.
Generous welfare systems tend to get gamed. That's what's hurting many counties in Europe right now - God only knows about a few years time when those pension/health deficits become unsurmountable. You can't do that and not tax. Scandinavian countries do both - pretty well, but they have a population for whom the notion of high taxation isn't seen as punitive. Third-world they are categorically not.
The appetite for that kind of thing across the Atlantic is limited. But wait. Not all Government spending is welfare, and those who would advocate for example unregulated business, minimal legislation etc don't seem to understand the wider consequences of what would happen if that were implemented. Governments spend money on legislation, infrastructure, social contracts to ensure that even private firms hired to get those basic, unnoticeable things right, get them right.
The example to hold up of an unlegislated business environment is not an idealised, small-government US; it is Yeltsin's Russia - and to some extent, the smash-and-grab Poland of the early 90s. No-one in their right mind wants that. It's easy to forget that Governments can and do provide a framework where you can trust the other guy enough to sign a meaningful contract with them. That framework costs, and it counts as spending on people.
The dole scroungers who could get off their arses and find work, not much sympathy there. Those incapacitated by health problems or temporarily removed from the job market because the closure of the local factory has ripped the heart out of the local community? Different matter, and those people deserve, at the least, our help.