What exactly do firms like Eastdil and CBRE do?

I'll try to explain as much as I can, but I've never worked for Eastdil/CBRE/JLL/PGIM, so hopefully another user with better experience can clarify further.

CBRE/JLL/Colliers etc: The big brokerage firms provide a range of services in the real estate industry such as capital markets, investment sales, valuation (commercial appraisal), and I think development consulting (whatever that is). But capital markets is just raising capital (debt or equity) for investors/developers. For example, my previous firm was in the process of stabilizing a 40 unit multifamily development and needed a permanent loan to take out the construction loan, so we hired CBRE to find us a lender(s). Investment Sales is pretty much just real estate brokerage but for much larger properties. In one of my previous real estate private equity internships, the firm I was interning for invested in new $50mm+ multifamily properties in the sunbelt states. We would receive dozens of Offering Memorandums (marketing material) for $50mm+, multi-hundred unit properties in Texas, Atlanta, Nashville etc... CBRE/JLL/Colliers was hired by the developer to sell these new developments for them and so they would put together a 50 page presentation to market the property and then send it to prospective buyers. Valuation is just that. Any time you get a loan from the bank, they will require an appraisal of the property so that they aren't giving you a loan that's worth more than the property.

Eastdil: I think Eastdil tries to market themselves as a prestigious real estate investment bank, but the services they offer are very similar to the big brokerage firms minus the valuations, property management, project management services. They stay on the "high finance" side of the business ie capital markets and investment sales. If you go to their website, they have a service called "Equity Sales," which is just investment sales, but they just want to make it sound "sexier" (I would also argue that investment sales is just a way of making "real estate brokerage" sound sexier too). I think Eastdil mainly works on the property level (selling and raising capital for individual properties) and not the corporate level (M&A and IPO for REITs). Public REITs would probably go to traditional investment banks for these services. When firms use the words real estate "advisory or consulting," it could really mean anything so you need to read the description. I've see "advisory/consulting" used for development consulting, capital advisory, lease structuring advisory etc...

PGIM/John Hancock/Metlife: These companies are large insurance companies with a butt ton of money to invest and so they open an in-house investment arm. PGIM is the investment management arm for Prudential Financial. I would say the main difference with these investment management companies and the megafund REPE shops is the types of investments they make and the amount of risk they take. Traditionally these companies are very low-risk because the funds they are managing are attached to people's lives. For example, if you buy life insurance from Prudential and they invest in many highly speculative development projects that all go bust, they just lost the funds that they would use to pay out your life insurance. However, it also doesn't  make financial sense for these companies to collect premiums from their customers and just keep it in cash at the bank. Instead, they invest the billions of dollars that they have in low-risk investments such as triple A bonds or in this case, stabilized properties. Often times, these companies are great for permanent loans to take out construction loans. So lets say that you are a developer and you need financing. You might go to Blackstone for a construction loan because Blackstone is willing to take on the higher construction risk (at a higher interest rate of course). Once construction is complete and you've stabilized the property, then you may seek PGIM to provide you with a permanent loan to take Blackstone out. PGIM makes a safe investment with solid return, Blackstone got repaid and made a nice return on the construction loan, and you were able to complete the development and got a permanent loan at a decent rate. Everyone's happy

Blackstone/Other megafunds: As I mentioned above, what I think is the main difference between the megafunds and Life Insurance investment arms is their risk tolerance and type of investments. Blackstone will make riskier investments in order to achieve higher returns. They may invest (either debt or equity) in ground up developments, value-add projects, or distressed deals. You can read up on a lot of their investments such as their acquisition of Stuy Town in NYC after Tishman and Blackrock defaulted.

Yes,  Eastdil is a brokerage company like CBRE. CBRE, JLL, Cushman & Wakefield, etc are all much bigger companies than Eastdil, however they all have more business lines. "Investment Sales" is simply selling a building. If you own, for example, an office building that you would like to sell, you hire one of these companies as your broker, just like you would hire a real estate agent when selling your house. 

Brokerage shops are losing flavor so they’re trying to rebrand themselves as “investment sales”, “equity/debt placement”, “capital markets”, or “advisory”. I just wish they’d stop the crap and say who they really are - which is a fancy brokerage firm.