In science there's always a misuse of the two terms. I know that lactate is the conjugate base of lactic acid.
Why are they used like is the same thing? For exemple: in lactic acid bacteria (LAB) fermentation it's often said that anaerobic glycolysis produces lactic acid, but if you actually look at the reaction it produces lactate.
Is this relevant? Because lactate is a negative compound while lactic acid is a neutral one.
If you were to produce any lactic acid in the body, it would pretty much immediately get deprotonated, so by right it's always going to be lactate. The $\mathrm pK_\mathrm{a}$ of a typical carboxylic acid is at most 5, and at physiological pH levels (~ 7, give or take) the ratio of $\ce{HA}:\ce{A-}$ is on the order of $1:100$. (As getafix mentioned, lactic acid is somewhat more acidic than usual, because of the electron-withdrawing hydroxyl group, so the ratio would be expected to be even larger. But these are just meant to be very rough numbers, for illustration.)
You could say that it's sloppiness on the part of the biologists, but past a certain point you don't really care whether it's $\ce{HA}$ or $\ce{A-}$, and that's why the distinction isn't really enforced. From a biochemical perspective the more important thing is the oxidation state as well as other byproducts (ATP, carbon dioxide, etc.) Likewise the citric acid cycle is called that despite citrate being the actual compound in the cycle.
And perhaps the most egregious case of sloppiness: DNA stands for deoxyribonucleic acid, but in the body the phosphate groups are deprotonated, so chemically speaking it really should be called the conjugate base of DNA: "deoxyribonucleate". But again, nobody really cares - as long as we know that it has a negative charge, we can call it by a strictly incorrect name and it's fine.
There are probably tons of physicists out there who hate us chemists for using non-rigorous terminology, too!
I was once given this "rule of thumb" in a biochem class:
If the $\mathrm{pH}$ of a solution is one or more units below the $\mathrm{p}K_\mathrm{a}$ of a group, then said group is protonated and if it is one or more unit above, then the group is de-protonated"
If you are anything like me, then you probably don't like rule of thumbs without some form of derivation/justification, then read the discussion here
According to this table, the $\mathrm{p}K_\mathrm{a}$ of lactic acid is $3.86$. Assuming, physiological $\mathrm{pH}$ hovers around ca. $7$, we notice that since $\mathrm{pH}>\mathrm{p}K_\mathrm{a}$, lactic acid would be found in its depronated form, i.e as lactate.
I would say using the terms interchangeably is sloppy use of terminology on the biochemists' part, and nothing more.
Is this relevant?
I would say relevance would depend on context. However, I would assume most biochemists/biologists are aware of the distinction, yet (for some reason unknown to me) continue to be sloppy in their use of terminology.
Lactic acid and lactate are part of an equilibrium reaction in aqueous solution. Even when the pH is far away from the pKa, there is still a small fraction of the minor species, and protonation/deprotonation reactions occur. If lactate were a bunny and the hydrogen ions in solutions were hats, lactic acid would just be the bunny after putting on the hat. If you were to do some analytical chemistry with a biological sample, you might have the lactic acid/lactate in a different solvent or at different pH, so you might talk about it as lactic acid or lactate depending on circumstances.
The animation conceptually shows how the major species changes with pH. It does not show the minor species.
