“Colloquially, a false equivalence is often called "comparing apples and oranges." This fallacy is committed when one shared trait between two subjects is assumed to show equivalence, especially in order of magnitude, when equivalence is not necessarily the logical result. False equivalence is a common result when an anecdotal similarity is pointed out as equal, but the claim of equivalence does not bear scrutiny because the similarity is based on oversimplification or ignorance of additional factors.” - False Equivalence/Wikipedia 

Note that the accusation of false equivalence is based on inference - that one knows what the other party is getting at when comparing x to y. But to say that x and y are basically the same thing, or not, begs the question: “in terms of what?” In other words, what set of facts associated with x and y are being compared? For example, consider the following accusation of false equivalence:

“Ms. Parker asserted that “the Democratic Party has moved as far left as the GOP has moved to the right.” This is a false equivalence and errant nonsense. The ultimate proof is that the Democrats chose Joe Biden, hardly anyone’s idea of a fire-breathing socialist, as their 2020 standard-bearer.” - Excerpt from A false equivalence on Democrats, Letter to the Editor from David R. Andrews in the Washington Post  

The set of facts important to the above letter writer appears to be who the president is and what’s his political agenda. But was that what Ms. Parker was thinking when she made her comparison? Maybe she was referring to shifts in party platforms; or the types of laws being passed by legislators; or the power dynamics among Democrats and Republicans and which factions are increasingly calling the shots in terms of legislation and candidates. I don’t know what she meant and so can’t pronounce judgement on whether her reasoning is flawed.

Then again, false equivalence is much more than a matter of flawed reasoning or cognitive bias.  Comparisons reflect an understanding of how the world works, what leads to what and over what time frame. A problematic comparison may stem from empirical error, logical error, or both. But people rarely hold themselves to some scientific standard of accuracy. Sometimes a comparison is made to serve a larger point and it’s not really advancing the conversation by nitpicking minor errors. Forest through the trees, and to see the forest you have to try to see what they’re seeing. What’s their Big Picture? That’s often a very hard question to answer.

Now for another example. First, some background. In 2020, Congress passed the Paycheck Protection Program (PPP), which provided loans to help businesses keep their workforce employed during the COVID-19 crisis. PPP loans made to eligible borrowers qualified for full loan forgiveness if during the 8- to 24-week covered period following loan disbursement: 1) employee and compensation levels were maintained; 2) the loan proceeds were spent on payroll costs other eligible expenses; and 3), at least 60% of the proceeds were spent on payroll costs. The PPP program ended on May 31, 2021. 

Earlier this year, President Biden compared his student loan forgiveness program to PPP loan forgiveness, in an attempt to highlight the hypocrisy of Republicans who had criticized the program:

“In a series of tweets, the White House highlighted several congressional Republicans…who it said had six- and seven-figure PPP loans forgiven as part of a federal program intended to help those harmed by the coronavirus.” - White House shines light on Republicans who are criticizing student debt cancellation after getting their PPP loans forgiven, Zoë Richards/NBC News  

Republicans responded:

“Comparison between student loan giveaway and loans to small businesses to stay afloat after forced lockdowns is ludicrous.” Fact Check: Biden Draws False Equivalence between PPP Loans and Student Loan Giveaway, GOP/Ways and Means Committee, House of Representatives. August 26, 2022

So if business owners who had previously been forgiven their PPP loans subsequently criticize Biden’s student loan forgiveness program, does that mean they’re hypocrites? Only if both loan forgiveness programs serve the same policy goal. Is this the case? If not, comparing them as Biden did would be to draw a false equivalence.