In addition to that, there is a third species of company that seems to be especially common in my industry (telecom): the nominal tech company. This is a company whose business model theoretically makes big engineering demands; it may not be a software company per se, but operating and gluing together tech is unquestionably the core mission behind its products and services. Yet, instead it's an overwhelmingly sales-driven company that mostly just pays lip service to engineering.
This type of company is insidiously bad for an engineering career because it has the outward appearance of being tech-focused. It's only with time that you realise that 80% of the staff hold management titles and do little but parry e-mail and hold meetings, that there are 20 VPs (in a company of a few hundred or a few thousand) who are usually on golf junkets, and the agenda is set mostly by blinged-out, testosterone-amped sales execs and the MBA frat boys who supposedly run sophisticated development and infrastructure groups. A tell-tale sign of such companies is that underneath ten layers of "management", you'll find three H1-Bs stuck somewhere in the back, sharing a cube, who are the only ones in the company who actually know anything about the technology. They are critical to the company, but because of their indentured H1-B status, the company is equally critical to them.
In the short term, working for such companies can be really cool. They usually have severe problems retaining serious engineering talent, so if you walk in there with substantial skills, they'll think you walk on water when you bang out a few lines of Bash or Python for basic housekeeping tasks. But you'll soon notice very high churn, or, at the other extreme, lots of people who have been there 10-20 years and have become deeply entrenched maintenance specialists in the company's internal systems and processes. This looks like tech work to them and others, but robs them of portable marketable skills. The moment they are laid off, they'll find that the world has moved on and that they have vanishingly little to offer other employers.