Is a 'seed phrase' independent of the type of wallet?
First of all, some software wallets imports are supporting only 12 word or 24 word combinations. 
Some support different BIPs and thus path derivation schemes (32/44/84) by default, and some only single one of them. 
Some have additional feature for a specific seed passphrase. 
All of the differences you can check on https://walletsrecovery.org/ 

So to answer your question, you have to install the wallet that uses the same seed format and path derivation as the one you've originally created.