Here after 5. Nc3 it's already a normal 4. e3 Tarrasch. The main difference of 4. e3 lines is that in some of them it's White who gets the isolated queen's pawn, not Black (eg. 5... dxc4 6. Bxc4 cxd4 7. exd4 - after 6... a6 we're in the old main line of the Queen's Gambit Accepted). Now remains the question of 1. d4 d5 2. c4 e6 3. Nf3 c5 vs 3. Nc3 c5. One point is that the Henning-Schara 4. cxd5 cxd4 isn't really playable against 3. Nf3. Another is that White can postpone Nc3 after 4. cxd5 exd5, like with 5. Bg5!? Be7 6. Bxe7 Nxe7 7. dxc5 and Black does not have a dynamic position.
Tarrasch and Pseudo-Tarrasch Defence

Here after 5. Nc3 it's already a normal 4. e3 Tarrasch. The main difference of 4. e3 lines is that in some of them it's White who gets the isolated queen's pawn, not Black (eg. 5... dxc4 6. Bxc4 cxd4 7. exd4 - after 6... a6 we're in the old main line of the Queen's Gambit Accepted). Now remains the question of 1. d4 d5 2. c4 e6 3. Nf3 c5 vs 3. Nc3 c5. One point is that the Henning-Schara 4. cxd5 cxd4 isn't really playable against 3. Nf3. Another is that White can postpone Nc3 after 4. cxd5 exd5, like with 5. Bg5!? Be7 6. Bxe7 Nxe7 7. dxc5 and Black does not have a dynamic position.
Interesting!
The difference is "Tarrasch" is a real opening name, and "Pseudo-Tarrasch" is not a real opening name. The opening you played is the Tarrasch, just as you thought.

At the position after 3...c5 on lichess opening explorer:
"D30 Queen's Gambit Declined: Tarrasch Defense, Pseudo-Tarrasch"
and chess.com opening explorer gives it the shorter name
"Queen's Gambit Declined: Pseudo-Tarrasch Defense"
And then by move 5 this changes to "Tarrasch 4.e3 Nf6 5.Nf3" (even though it was a different move order)
There's no Pseudo-Tarrasch, that's just a pseudo-name given by someone with a database and too much time on their hands, then copied from the same source by both lichess and chess.com, and probably others. There are so many bogus names in the opening explorers, it's not worth worrying about.

I'm not worried just curious. The names are based on the Encyclopedia of Chess Openings.
https://www.chessjournal.com/eco/
There is
D30 | Pseudo-Tarrasch, QGD | d4 d5 c4 e6 Nf3 c5 |
and also
D50 | Pseudo-Tarrasch Variation, QGD | d4 d5 c4 e6 Nc3 Nf6 Bg5 c5 cxd5 |
The ECO is language-less, it gives the codes (D30) but does not name the openings. In any case the names might differ by language or country. Names are conventional, but Pseudo-Tarrasch is not one of the conventional names, it's just a mistake. I actually do know the individual who gave this wrong name Pseudo-Tarrasch, but I am purposely not naming this person because it is not important for the discussion. What's important is to know that just because some site or app on the internet says the name of D30 is Pseudo-Tarrasch, doesn't make it so. Even if *all* sites and apps on the internet say that, doesn't make it so, especially if they all derive from the same mistaken source.

Why do you say it is a mistake? There are many openings that have pseudo variants:
A00 | Pseudo-Diemer Gambit, Dunst | Nc3 d5 e4 dxe4 f3 exf3 Qxf3 |
D06 | Pseudo-Slav, QGD | d4 d5 c4 Bf5 Nc3 e6 Nf3 c6 |
D06 | Pseudo-Chigorin, QGD | d4 d5 c4 Bf5 Nc3 e6 Nf3 Nc6 |
D30 | Pseudo-Meran; Semi-Slav, QGD | d4 d5 c4 e6 Nf3 Nf6 e3 c6 |
D02 | Pseudo-Catalan | d4 d5 Nf3 Nf6 g3 |
A40 | Pseudo-Saemisch | d4 g6 c4 Bg7 e4 d6 Be3 Nf6 f3 |
A57 | Pseudo-Saemisch, Benko Gambit | d4 Nf6 c4 c5 d5 b5 f3 |
A46 | Pseudo-Benko Gambit | d4 Nf6 Nf3 c5 d5 b5 |
A48 | Pseudo-King’s Indian Variation; A48 | d4 Nf6 Nf3 g6 |
C88 | Pseudo-Marshall Var, Ruy Lopez | e4 e5 Nf3 Nc6 Bb5 a6 Ba4 Nf6 O-O Be7 Re1 b5 Bb3 Bb7 c3 d5 exd5 Nxd5 Nxe5 Nxe5 |
B06 | Pseudo-Austrian Attack | e4 g6 d4 Bg7 Nc3 d6 f4 |
B00 | Pseudo-Spanish Variation | e4 Nc6 Bb5 |
Do you disagree with some/all of these other pseudo classifications?
What characteristic makes an opening "pseudo"?
....... Another is that White can postpone Nc3 after 4. cxd5 exd5, like with 5. Bg5!? Be7 6. Bxe7 Nxe7 7. dxc5 and Black does not have a dynamic position.
Agree- but I'll add that (IMO) black also gets easy equality in the lines after whites Nf3&Bg5. -Bill

If everyone agrees that a word means a thing then it does mean that thing, that's how language works.

chess.com’s opening recognition system is having a heart attack rn, it said the starting position of the Najdorf Sicilian was the Anti-English Variation and that the QGD was the English Opening
I played an OTB friendly game last night that opened like this:
I thought I was playing the Tarrasch but the opening explorer says it is the Pseudo-Tarrasch. What are the differences?