
From their first appearance in Tintin in the Congo—serialized May 1930 to June 1931—Thomson and Thompson have been hard to tell apart.
Benoît Peeters got it wrong in Tintin and the World of Hergé. On page 59, Peeters writes “Identical in every way, the two can only be determined by the style of their moustaches: Thomson’s is more rounded and Thompson’s more pointed.”
Herge: The Man Who Created Tintin by Pierre Assouline also gets it backward: “They are absolutely indentical in appearance (black suits, bowler hats, and canes) but can be distinguished by their mustaches. The mustache tips of Thompson (with a p) rise, and those of Thomson (without a p) dip.”
But as our tableau clearly shows, Thompson, with a p, has the rounded mustache and Thomson, without a p, has the pointy mustache. Tintin.com agrees: “Thompson's (X33) is neatly trimmed, whilst Thomson's (X33A) has a distinctive twirl at the ends.” The Tintin Games Book also correctly identifies Thomson and Thompson.
The two detectives were originally called X-33 and X-33 bis in French, which appears in early English translations as X-33 and X-33A.
The early names may be related to the fictional Frau Marie Kolverer, Agent X-27, (played by Marlene Dietrich) in “Dishonored,” a 1931 romantic spy film by Josef von Sternberg. The Kolverer character was inspired by the real spy Mata Hari, codename Agent H-21, and arrested as a German agent in 1917. Or maybe it’s just coincidence.
The two characters were later named Dupont and Dumond in French and Thomson and Thompson in English translations.
Thomson and Thompson appear in only one frame of The Shooting Star, on page 20.
They appear on a 2007 French stamp and a 1943 serialised story “Thomson & Thompson, Detectives,” by Paul Kinnet and illustrated by Hergé.

X33 and X33 bis from the black and white early version of Cigars of the Pharaoh

Thompson and Thomson’s first appearance, in Tintin in the Congo.
In the 1930-31 version (colorized) in the iPad Tintin set, the two characters standing near the train are railroad attendants.

Cigars of the Pharaoh
page 3, frame 13

The Black Island
page 2, frame 7

The Crab with the Golden Claws
page 49, frame 7

The Crab with the Golden Claws
page 59, frame 10

The Seven Crystal Balls
page 18, frame 8

The Seven Crystal Balls
page 48, frame 13

The Land of Black Gold
page 6, frame 14

The Land of Black Gold
page 35, frame 11

Destination Moon
page 24, frame 4

Explorers on the Moon
page 4, frame 9

Explorers on the Moon
page 17, frame 7

The Castafiore Emerald
page 30, frame 7

The Castafiore Emerald
page 47, frame 2

The Castafiore Emerald
page 60 frame 11

Tintin and the Picaros
page 60 frame 2

Tintin and the Picaros
page 60 frame 6

Prisoners of the Sun
page 9, frames 10 and 11

The Calculus Affair
page 14, frame 3

The Red Sea Sharks
page 7, frames 12 and 13
To be precise: Unless the Thom(p)sons themselves are consistently confused about their own identities, and Captain Haddock is equally confused, Thomson (without a p) has the pointy mustache and Thompson (with a p) has the droopy mustache.
That’s our opinion and we’re stuck with it.