Is there a difference between short and long term loss?
I want to dump a stock I bought last month.

If you hold a stock for more than a year and then sell it you have a long term gain or loss. If you sell the stock you bought last month for a loss, you have a short term loss.

In other words, NO, there is NO practical difference between a long-term and a short-term loss.

Short term gain is taxed as your ordinary income, while long term gain is taxed at 5% or 15% tax rate.

That is true about gain, but question was about LOSS.

On schedule D, any short term loss will first offset the short term gain. Similarly, long term loss will first offset the long term loss.
Many times if you must sell stocks at a loss and it is nearing a year, it is better to have a short term loss, so that your total short term income reduces, while longterm income remains unchanged.

MukatA:

Here is the process:

Short-term loss offsets short-term gain, while long-term loss offsets long-term gain.

Then, if there is ANY loss left, short-term loss will offset LONG-term gain or long-term loss will offset SHORT-term gain.

If there is short-term gain left, it is taxed as ordinary income.

If there is long-term gain left, it is taxed at capital gains rates, either 5% or 15%.

If there is EITHER short-term or long-term LOSS left, it can be used to offset other income, up to $3,000 per year.

Any loss in excess of $3,000 is carried forward to the next year, where the entire process starts over again.

I have clients who experienced stock losses in excess of $250,000 from the last stock market crash of 2000-2001. It may take them the rest of their lives to be able to write off those losses.