There are a few significant differences between a Pi and an Arduino hardware interface wise:
The Arduino uses 5V logic whereas the Pi uses 3.3V logic. Some sensors can be used either way, powered by 5V (the Pi can provide 5V power) and either 3.3 or 5V logic (sometimes they can be powered either way as well). Some, however, they are either one way or the other, and logically enough ones sold for use with an Arduino will often be 5V only.
This does not mean you cannot use them, but you will need to use a level shifter as described in this answer.
Arduinos have a number of analog inputs, whereas the Pi has none. Many sensors use an analog output, i.e., variable voltage. This means a single pin can report a continuously varying value, and the Arduino can read this with 10 bit precision (i.e., 0 - 1023). The GPIOs on the Pi are all digital, meaning their value is binary, either on/high or off/low (i.e., a value with 1 bit precision, 0 or 1).
You can however attach an ADC (analog-to-digital converter) chip (e.g., in breadboard friendly DIP form) to a Pi via one of the serial buses (SPI or I2C; I do not think there are any converters that use UART). I believe they may also be available with a parallel pin output, where for each pin you get 1 bit of resolution; this would occupy a lot of GPIOs though.
Finally, you can connect an Arduino to a Pi via a serial bus (generally UART or I2C) and use it to interface with 5V and/or analog devices. Arduino nano clones -- Arduino is actually an open hardware platform, meaning anyone can make and distribute them -- are probably cheaper and easier to acquire online than ADC chips, and provide more functionality and flexibility (unless you need greater than 10-bit analog precision). The major drawback would be that even the nano is quite a bit bulkier than a DIP ADC.
looking around on Amazon I found a lot of extremely similar looking sets that read Starter Kit for Raspberry Pi 3
That kit looks to have a number of analog sensors, but it also includes an ADC, an ADC 0832, which has 8-bit resolution, 2 inputs, and (if it matches that TI spec), a microwire protocol interface. I have never used the latter but it looks to be SPI compatible, so should work with a Pi (presumably the people selling the kit would not include it otherwise).