"Adjusted XP" is for determining encounter difficulty; actual XP is what you give to the party for beating the encounter

The difference between XP and adjusted XP in determining the difficulty of a combat encounter is explained in the guidelines on building combat encounters on Basic Rules p. 165 or in the corresponding section on DMG p. 82.

Step 1 and 2 of evaluating encounter difficulty is to determine individual XP thresholds and then add them to get the party's XP thresholds. Step 3 is to simply add up the monsters' XP, giving you the regular experience totals for the encounter. Then comes Step 4:

4. Modify Total XP for Multiple Monsters. If the encounter includes more than one monster, apply a multiplier to the monsters’ total XP. The more monsters there are, the more attack rolls you’re making against the characters in a given round, and the more dangerous the encounter becomes. To correctly gauge an encounter’s difficulty, multiply the total XP of all the monsters in the encounter by the value given in the Encounter Multipliers table.

For example, if an encounter includes four monsters worth a total of 500 XP, you would multiply the total XP of the monsters by 2, for an adjusted value of 1,000 XP. This adjusted value is not what the monsters are worth in terms of XP; the adjusted value’s only purpose is to help you accurately assess the encounter’s difficulty.

When making this calculation, don’t count any monsters whose challenge rating is significantly below the average challenge rating of the other monsters in the group unless you think the weak monsters significantly contribute to the difficulty of the encounter.

\$\begin{array}{|c|l|} \hline \textbf{Number of Monsters} & \textbf{Multiplier} \\ \hline 1 & × 1 \\ 2 & × 1.5 \\ 3–6 & × 2 \\ 7–10 & × 2.5 \\ 11–14 & × 3 \\ 15 \text{ or more} & × 4 \\ \hline \end{array} \$

In short: adjusted XP determines the true difficulty of the encounter, considering action economy. Regular XP is the actual amount given to the party for beating the encounter.

5e co-creator Mike Mearls explains the reasoning here:

Hi Mike. Players are asking me why actual xp is given instead of adjusted xp. What was design purpose of this?

it's kind of hacky - adjusted XP is there only for comparing difficulty. it's not "real" XP.

Making me wonder what "xp" represents now.

the system really shouldn't use XP as a measure - it muddies the issue of its meaning.

Thanks for the reply! If adjusted xp says something is more difficult, shouldn't players get more xp then?

not necessarily - the system is trying to capture the inherent difficulty in fighting more than 1 foe

2 years earlier, he also responded to a question asking about house-ruling that the amount of XP given out was equal to adjusted XP:

Thinking of houseruling that adjusted encounter XP = actual XP. Any reason why this isn't RAW? Any pitfalls to be aware of? Thx!

it makes hordes of weaker creatures a more appealing fight, if players metagame that. not game breaking