They're very similar, and when I cooked Ancient Roman recipes I used Thai fish sauce (nam pla, Squid Brand) in place of liquamen (garum). Nuoc mam is much the same thing as nam pla. So is colatura, which is still made in Italy.

Though there was indirect contact with China, from where they obtained silk, and India, from where they obtained pepper, I'm unaware of any direct contact between Ancient Rome and South East Asia, and I'm skeptical the recipe somehow made its way as far as Vietnam and Thailand. I think it's more likely they arrived at the same recipe independently.

Here's the production method for liquamen. It was done on an industrial scale and listed as an ingredient in the recipes of Apicius:

From A Taste of Ancient Rome, p. 27:

Ancient sources contain countless recipes for the preparation of garum, also known as muria or liquamen. The most complete is provided by Gargilius Martialis, a writer from the third century A.D.

Use fatty fish, for example sardines, and a well-sealed (pitched) container with a 26-35 quart/liter capacity. Add dried aromatic herbs possessing a strong flavor, such as dill, coriander, fennel, celery, mint, oregano, and others making a layer on the bottom of the container; then put down a layer of fish (if small leave them whole, if large use pieces); and over this add a layer of salt two fingers high. Repeat these three layers until the container is filled. Let it rest for seven days in the sun. Then mix the sauce daily for twenty days. After that time it becomes a liquid (garum).

-- Gargilius Martialis, De medicina et de virtute herbarum

From "Geoponica" (20.46.1-6), as cited by Robert I. Curtis, Garum and Salsamenta: Production and Commerce in Materia Medica (New York: E. J. Brill, 1991):

The so-called liquamen is made in this manner: the intestines of fish are thrown into a vessel and salted. Small fish, either the best smelt, or small mullet, or sprats, or wolffish, or whatever is deemed to be small, are all salted together and, shaken frequently, are fermented in the sun.
After it has been reduced in the heat, garum is obtained from it in this way: a large, strong basket is placed into the vessel of the aforementioned fish, and the garum streams into the basket. In this way the so-called liquamen is strained through the basket when it is taken up. The remaining refuse is alex.
The Bithynians prepare it in this manner: It is best if you take small or large sprats, but if not, wolffish, or horse-mackerel, or mackerel, or even alica, and a mixture of all, and throw these into a baker's kneading trough, in which the are accustomed to knead meal. Tossing into the modius of fish two Italian sextarii of salt, mix up thoroughly in order to strengthen it with salt. After leaving it alone for one night throw it into a vessel and place it without a lid in the sun for two or three months, agitating it with a shaft at intervals. Next take it, cover it, and store it away.
Some add to one sextarius of fish, two sextarii of old wine.
Next, if you wish to use the garum immediately, that is to say not ferment it in the sun, but to boil it, you do it this way. When the brine has been tested, so that an egg having been thrown in floats (if it sinks, it is not sufficiently salt), and throwing the fish into the brine in a newly-made earthenware pot and adding in some oregano, you place it on a sufficient fire until it is boiled, that is until it begins to reduce a little. Some throw in boiled-down must. Next, throwing the cooled liquid into a filter you toss it a second, and a third time through the filter until it turns out clear. After having covered it, store it away.
The best garum, the so-called haimation, is made in this way: the intestines of tunny along with the gills, juice and blood are taken and sufficient salt is sprinkled on. After having left it alone in the vessel for two months at most, pierce the vessel and the garum, called haimation, is withdrawn.