I think this confusion is coming from over-generalized terms that have worked their way into the vernacular of many real estate professionals.
A title insurance company is usually a very large, publicly-traded company that underwrites and issues title insurance policies in real estate transactions. Examples of title insurance companies are Fidelity, First American, Old Republic, Chicago Title and Stewart Title.
A title agency is a much smaller office that serves a local market by handling the title research, preparing paperwork, facilitating closings and collecting/holding/transferring funds in a real estate transaction.
Here’s where the terminology starts to get muddled:
Many of the big title insurance companies also have their own title agency branches. For example, Chicago Title, Stewart Title and First American are not only title insurance companies, they also have title agency offices around the country (the brick-and-mortar place where you go to sign documents and either deliver a check or collect a check).
However, there are also many independently operated title agencies that are NOT owned and operated by one of the big title insurance companies. These independent agencies can choose to work with one or more of the above-mentioned title insurance underwriters to provide title insurance policies to their customers, but all of the hands-on work of closing real estate transaction (title searches, preparing closing documents, getting documents signed, collecting and transferring funds, etc) is done by the independently operated title agency.
When someone uses the term “title company”, they could be referring to either a title insurance company or a title agency, or both. Most often, I’ve found they are referring to the title agency (because that’s who they are working with directly to get the deal closed, not the underwriting office), but it ultimately depends on the context of what is being said and who is saying it.
An escrow agency (also known as an “escrow office” or “escrow company”) is essentially the same thing as the title agency described above. It’s the branch office that handles the facilitation of closing, including everything from title searches to paperwork preparation to scheduling closing meetings and transferring funds between all parties.
In some circles, people refer to their closing agent using the word “escrow” and in other circles they use the word “title”.
I personally think “escrow” is a better describer word for the local branch, because “title” is more of an umbrella term that could be referring to one of a few different things. “Escrow” is only ever used for the local office that is literally holding the funds in escrow and doing 90% of the work of closing deals.